21. Q21a
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Similar Question 1
<p>Solve.</p><p><code class='latex inline'>\log x=4</code></p>
Similar Question 2
<p>Solve.</p><p> <code class='latex inline'>\log_2x=2\log_25</code></p>
Similar Question 3
<p>Mental Math Solve each equation.</p><p><code class='latex inline'>\displaystyle \log _{8} 2=x </code></p>
Similar Questions
Learning Path
L1 Quick Intro to Factoring Trinomial with Leading a
L2 Introduction to Factoring ax^2+bx+c
L3 Factoring ax^2+bx+c, ex1
Now You Try
<p>Solve each equation. Check your answers.</p><p><code class='latex inline'>\displaystyle 2 \log (x+1)=5 </code></p>
<p>Solve.</p><p>e) <code class='latex inline'>3\log x-\log3=2\log3</code></p>
<p>Prove that <code class='latex inline'>a, b</code>, and <code class='latex inline'>c</code> are 3 numbers that form a geometric sequence if and only if <code class='latex inline'>\log_xa</code>, <code class='latex inline'>\log_xb</code> and <code class='latex inline'>\log_xc</code> form an arithmetic sequence.</p>
<p>Evaluate, rounding to three decimal places, if necessary. </p><p>a) <code class='latex inline'>e^{-3}</code></p>
<p>Describe the strategy that you would use to solve each of the following equations. (Do not solve.)</p><p> <code class='latex inline'>\log_9x=\log_94+\log_95</code></p>
<p> Solve the equation.</p><p><code class='latex inline'> \displaystyle \log_{2}(\log_{3}x) = 4 </code></p>
<p>Solve and check for extraneous roots. Where necessary, round answers to 2 decimal places.</p><p><code class='latex inline'>\displaystyle 4^x = 3 +18(4^{-x}) </code></p>
<p>Solve each equation. Leave answers in exact form.</p><p><code class='latex inline'>\displaystyle 2^x = 3^{x -1} </code></p>
<p>Solve.</p><p> <code class='latex inline'>\log_5(2x-4)=\log_536</code></p>
<p>Solve each equation. Check your answers.</p><p><code class='latex inline'>\displaystyle \log 6 x-3=-4 </code></p>
<p>Describe the strategy that you would use to solve each of the following equations. (Do not solve.)</p><p> <code class='latex inline'>\log x-\log2=3</code></p>
<p>Solve the equation <code class='latex inline'>\displaystyle 2\log(x + 11)= (\frac{1}{2})^x</code>.</p>
<p>Solve.</p><p><code class='latex inline'>\displaystyle \log(4x - 1) = \log(x + 1) + \log 2 </code></p>
<p>Solve for <code class='latex inline'>t</code>. Round answers to two decimal places.</p><p><code class='latex inline'>\displaystyle 3 = 1.1^t </code></p>
<p>Use natural logarithms to solve each equation.</p><p><code class='latex inline'>\displaystyle e^{\frac{x}{2}}=5 </code></p>
<p>Solve for x.</p><p><code class='latex inline'> \displaystyle 2\log_x{25} - 3 \log_{25}x = 1 </code></p>
<p>Solve each equation. Check your answers.</p><p><code class='latex inline'>\displaystyle \log (3 x+1)=2 </code></p>
<p> Solve the equation.</p><p><code class='latex inline'> \displaystyle 2\log x = \log 2 + \log(3x - 4) </code></p>
<p>Solve each equation. Leave answers in exact form.</p><p><code class='latex inline'>\displaystyle 8^{x+ 1} = 3^{x-1 } </code></p>
<p> Solve the equation.</p><p><code class='latex inline'> \displaystyle x^{\log x} =10 </code></p>
<p>Solve for x.</p><p><code class='latex inline'> \displaystyle \log_{x} 0.125 = - 2 </code></p>
<p>Solve. </p><p><code class='latex inline'> \displaystyle \log\sqrt{2k +4} = 1 + \log k </code></p>
<p>If <code class='latex inline'>\displaystyle{\log\left(\frac{x+y}{5}\right)=\frac{1}{2}(\log x+\log y)}</code>, where <code class='latex inline'>x>0</code>, <code class='latex inline'>y>0</code>, show that <code class='latex inline'>x^2+y^2=23xy</code></p>
<p>Given <code class='latex inline'>\log_2a+\log_2b=4</code>, calculate all the possible integer values of <code class='latex inline'>a</code> and <code class='latex inline'>b</code>. Explain your reasoning. </p>
<p>Solve for x.</p><p><code class='latex inline'> \displaystyle \log_{16}x + \log_4x + \log_2x = 7 </code></p>
<p>Solve.</p><p> <code class='latex inline'>\log_x625=4</code></p>
<p>Solve.</p><p><code class='latex inline'>\displaystyle \log(x + 9) - \log x = 1 </code></p>
<p>Solve.</p><p> <code class='latex inline'>\log_2x+\log_23=3</code></p>
<p>If <code class='latex inline'>\log_9x = \log_3y + 1</code>, determine <code class='latex inline'>y</code> as a function of <code class='latex inline'>x</code>.</p>
<p>Consider the equation <code class='latex inline'>\displaystyle10 = 2^x</code>.</p><p>Then <code class='latex inline'>10 = </code>?</p>
<p>Solve for <code class='latex inline'>x</code>, correct to two decimal places. </p><p><code class='latex inline'>9 = 3e^x</code></p>
<p>Solve for x.</p><p><code class='latex inline'>\displaystyle 2^{3 x-4}=5 </code></p>
<p>Find the roots of each equation. </p><p><code class='latex inline'>\log(x-2) = 1</code></p>
<p>Solve.</p><p><code class='latex inline'>\displaystyle \log 3x = 4 </code></p>
<p>State all restrictions ans solve.</p><p><code class='latex inline'>\displaystyle 3\log_{x^2-25}(x + 5) = 2 </code></p>
<p>Solve for x.</p><p><code class='latex inline'> \displaystyle \log9^{-1} + x\log\sqrt[3]{3^{5x - 7}} = 0 </code></p>
<p>Solve.</p><p> <code class='latex inline'>\log(x+2)+\log(x-1)=1</code></p>
<p>Solve.</p><p> <code class='latex inline'>\log(5x-2)=3</code></p>
<p>Explain why there are no solutions to the equations <code class='latex inline'>\log_3(-8)=x</code> and <code class='latex inline'>\log_{-3}9=x</code>.</p>
<p>Solve.</p><p><code class='latex inline'> \displaystyle 1 - \log(2x) = 0 </code></p>
<p> Solve.</p><p><code class='latex inline'>\displaystyle \log_4(x + 2) + \log_4( x-1) = 1 </code></p>
<p>Solve.</p><p> <code class='latex inline'>\displaystyle{\log_2x=\frac{1}{2}\log_23}</code></p>
<p> Solve the equation.</p><p><code class='latex inline'> \displaystyle \log_{5}x + \log_{5}(x + 1) = \log_{5}20 </code></p>
<p>Solve for the unknown.</p><p><code class='latex inline'>9 = \log_5(x + 100)+ 6</code></p>
<p>Solve.</p><p> <code class='latex inline'>\log_3(3x+2)=3</code></p>
<p>Solve for the unknown.</p><p><code class='latex inline'>5 = \log_2(2x - 10)</code></p>
<p>Solve.</p><p><code class='latex inline'>\log_x0.04=-2</code></p>
<p> Solve the equation.</p><p><code class='latex inline'> \displaystyle \log x + \log(x - 1) = \log(4x) </code></p>
<p>Solve for <code class='latex inline'>x</code>. State your answer in decimal, accurate to one tenth place.</p><p><code class='latex inline'> \displaystyle \log(3^{\sqrt{\frac{x(x- 4)}{x - 3} } + 1})= 1 </code></p>
<p>Solve.</p><p><code class='latex inline'>\displaystyle \log_5(2x - 1) =3 </code></p>
<p>Solve.</p><p> <code class='latex inline'>\displaystyle{\log_{\frac{1}{2}}x=-2}</code></p>
<p>Solve for x.</p><p><code class='latex inline'>\displaystyle \log x-\log 2=3 </code></p>
<p>Describe the strategy that you would use to solve each of the following equations. (Do not solve.)</p><p> <code class='latex inline'>\log x=2\log8</code></p>
<p>Solve <code class='latex inline'> \displaystyle \log_2x + \log_2(x + 2) = 3 </code>. Check for extraneous roots.</p>
<p>Evaluate, rounding to three decimal places, if necessary. </p><p>a) <code class='latex inline'>e^{ln(0.61)}</code></p>
<p>Solve.</p><p> <code class='latex inline'>\log(x-2)+\log_3x=1</code></p>
<p>Solve.</p><p><code class='latex inline'>\displaystyle \log\sqrt{x^2 -1} = 2 </code></p>
<p>If <code class='latex inline'>\displaystyle \log_x(e^a) = \log_ae</code>, where <code class='latex inline'>a \neq 1</code> is a positive constant, then <code class='latex inline'>x</code> equals</p><p><strong>A</strong> <code class='latex inline'>a</code></p><p><strong>B</strong> <code class='latex inline'>\frac{1}{a}</code></p><p><strong>C</strong> <code class='latex inline'>a^a</code></p><p><strong>D</strong> <code class='latex inline'>a^{-a}</code></p><p><strong>E</strong> <code class='latex inline'>a^{\frac{1}{a}}</code></p>
<p> Solve the equation.</p><p><code class='latex inline'> \displaystyle x^x = x </code></p>
<p>Mental Math Solve each equation.</p><p><code class='latex inline'>\displaystyle \log _{7} 343=x </code></p>
<p>Solve for <code class='latex inline'>x</code>, correct to three decimal places.</p><p><code class='latex inline'>1000 = 20e^{\frac{x}{4}}</code></p>
<p>Solve.</p><p><code class='latex inline'>\log x=4</code></p>
<p>Solve <code class='latex inline'>\displaystyle{\frac{\log(35-x^3)}{\log(5-x)}=3}</code>.</p>
<p> Solve the equation.</p><p><code class='latex inline'> \displaystyle x^2e^x + xe^x - e^x = 0 </code></p>
<p> Solve the equation.</p><p><code class='latex inline'> \displaystyle \log(x - 1) + \log(x + 2) = 1 </code></p>
<p>Solve.</p><p><code class='latex inline'>\displaystyle 8 \cdot 5^{2x} + 8 \cdot 5^x =6 </code></p>
<p>Use natural logarithms to solve each equation.</p><p><code class='latex inline'>\displaystyle e^{\frac{x}{9}}-8=6 </code></p>
<p>Solve for x.</p><p><code class='latex inline'>\displaystyle 5^x = 3125 </code></p>
<p>Consider the equation <code class='latex inline'>\displaystyle10 = 2^x</code>.</p><p>Solve the equation for x by taking the common logarithm of both sides.</p>
<p>Evaluate, rounding to three decimal places, if necessary. </p><p>a) <code class='latex inline'>ln(6.2)</code></p>
<p>Solve and check for extraneous roots. Where necessary, round answers to 2 decimal places.</p><p><code class='latex inline'>\displaystyle 3^ x + 1 +56(3^{-x}) = 0 </code></p>
<p>Find the roots of each equation. </p><p><code class='latex inline'>2= \log(x+ 25)</code></p>
<p>Find the roots of each equation. </p><p><code class='latex inline'>4 = 2\log(p + 62)</code></p>
<p>Solve. Express each answer to three decimal places.</p><p><code class='latex inline'>\displaystyle 6^x = 78 </code></p>
<p>Solve <code class='latex inline'>3^x = 15</code> by taking the common logarithm (base 10) of both sides.</p>
<p>Solve for <code class='latex inline'>t</code>. Round answers to two decimal places.</p><p><code class='latex inline'>\displaystyle 100 = 10(1.04)^t </code></p>
<p>Solve for <code class='latex inline'>x</code>.</p><p><code class='latex inline'>2^{2x}-3(2^{x+3})+128=0</code></p>
<p>Solve. </p><p><code class='latex inline'> \displaystyle \log\sqrt{x^2 - 3x} = \frac{1}{2} </code></p>
<p>Solve and check for extraneous roots. Where necessary, round answers to 2 decimal places.</p><p> <code class='latex inline'>\displaystyle 5^x = 3- 5^{2x} </code></p>
<p>Solve for <code class='latex inline'>t</code>. Round answers to two decimal places.</p><p><code class='latex inline'>\displaystyle 2= 1.07^t </code></p>
<p>Solve for x.</p><p><code class='latex inline'>\displaystyle 4^{x}=19 </code></p>
<p><code class='latex inline'>\displaystyle 1.5^{x}=356 </code></p>
<p>Solve.</p><p><code class='latex inline'>\log x=3\log2</code></p>
<p>If <code class='latex inline'>\displaystyle{\left(\frac{1}{2}\right)^{x+y}=16}</code> and <code class='latex inline'>\log_{x-y}8=-3</code>, calculate the values of <code class='latex inline'>x</code> and <code class='latex inline'>y</code>.</p>
<p>Mental Math Solve each equation.</p><p><code class='latex inline'>\displaystyle \log _{8} 2=x </code></p>
<p>Solve each equation. Check your answers.</p><p><code class='latex inline'>\displaystyle \ln (t-1)^{2}=3 </code></p>
<p>Solve for <code class='latex inline'>x</code>, correct to two decimal places. </p><p><code class='latex inline'> lnx= -5</code></p>
<p>Solve for <code class='latex inline'>x</code>, correct to three decimal places.</p><p> <code class='latex inline'>e^x = 5</code></p>
<p>Solve.</p><p> <code class='latex inline'>\log3+\log x=1</code></p>
<p>Solve for <code class='latex inline'>x</code>, correct to three decimal places.</p><p><code class='latex inline'>\ln(e^x) = 0.442</code></p>
<p>Solve.</p><p><code class='latex inline'>\log_5(2x-1)=2</code></p>
<p>Solve each equation. Check your answers.</p><p><code class='latex inline'>\displaystyle \log 2 x=-1 </code></p>
<p>Solve.</p><p><code class='latex inline'>\displaystyle \log_4(3x - 5) = \log_411 + \log_42 </code></p>
<p>Solve for x.</p><p><code class='latex inline'> \displaystyle \log_{3\sqrt{3}}\frac{1}{27} = x </code></p>
<p>Solve for the unknown.</p><p><code class='latex inline'>\log_8(t - 1)+ 1= 0</code></p>
<p>Solve.</p><p><code class='latex inline'>\displaystyle 4^x + 6 \cdot 4^{-x} = 5 </code></p>
<p> Solve the equation.</p><p><code class='latex inline'> \displaystyle 100(1.04)^{2t} = 300 </code></p>
<p>Solve for the unknown.</p><p><code class='latex inline'>\log_3(n^2-3n+5)= 2</code></p>
<p>Solve each equation. If necessary, round to the nearest ten-thousandth.</p><p><code class='latex inline'>\displaystyle 5^{3 x}=125 </code></p>
<p>Solve.</p><p><code class='latex inline'>3\log_2x-\log_2x=8</code></p>
<p>Find the roots of each equation, correct to two decimal places, using graphing technology. Sketch the graphical solution.</p><p><code class='latex inline'> \displaystyle \log(x + 2) = 2 - \log x </code></p>
<p>Solve for the unknown.</p><p><code class='latex inline'>\log_3(x+ 4) = 2</code></p>
<p> Solve the equation.</p><p><code class='latex inline'> \displaystyle \log_{9}(x - 5) + \log_{9}(x + 3) = 1 </code></p>
<p>Determine the acute angle <code class='latex inline'>x</code> that satisfies the equation</p><p><code class='latex inline'>\displaystyle \log_{2\cos x}6 + \log_{2\cos x}\sin x = 2</code></p>
<p>Solve.</p><p> <code class='latex inline'>\log(2x+1)+\log(x-1)=\log9</code></p>
<p>Use natural logarithms to solve each equation.</p><p><code class='latex inline'>\displaystyle e^{\frac{x}{5}}+4=7 </code></p>
<p>If <code class='latex inline'>a > 1</code>, <code class='latex inline'>b > 1</code>, and <code class='latex inline'>p = \frac{\log_b(\log_ba)}{\log_ba}</code>, then find <code class='latex inline'>a^p</code> in simplest form.</p>
<p> Solve the equation.</p><p><code class='latex inline'> \displaystyle x^{\log x +2} =1000 </code></p>
<p>Solve.</p><p> <code class='latex inline'>\log_2x=2\log_25</code></p>
<p>Solve for x.</p><p><code class='latex inline'>\displaystyle 5-3^{x}=-40 </code></p>
<p>Solve <code class='latex inline'>5^{x + 2} = 6^{x + 1}</code>. Round your answer to three decimal places.</p>
<p>Solve for <code class='latex inline'>t</code>. Round answers to two decimal places.</p><p><code class='latex inline'>\displaystyle 5 = 1.08^{t + 2} </code></p>
<p>Solve for x.</p><p><code class='latex inline'> \displaystyle \log_2(x - 1)^2 - \log_{0.5}(x - 1) = 9 </code></p>
<p>Solve each equation.</p><p><code class='latex inline'>\displaystyle 2 \log x+\log 4=2 </code></p>
<p> Solve the equation.</p><p><code class='latex inline'> \displaystyle x^{2- \frac{1}{2}\log x} = 100 </code></p>
<p>Solve for <code class='latex inline'>t</code>. Round answers to two decimal places.</p><p> <code class='latex inline'>\displaystyle 15 = (\frac{1}{2})^{\frac{t}{4}} </code></p>
<p> Solve the equation.</p><p><code class='latex inline'> \displaystyle (1.00625)^{12t} = 2 </code></p>
<p>Use natural logarithms to solve each equation.</p><p><code class='latex inline'>\displaystyle e^{2 x}=10 </code></p>
<p>Solve.</p><p> <code class='latex inline'>\log(x-5)=\log10</code></p>
<p>Let [x] represent the greatest integer less than or equal to x. For example, <code class='latex inline'>[4.9] = 4</code> If <code class='latex inline'>n = 623, 324, 121, 314, 872, 902, 375, 721</code> what is the value of </p><p><code class='latex inline'> \displaystyle [\frac{n}{10^{[\log n]}}] </code></p>
<p>Solve.</p><p><code class='latex inline'>\displaystyle \log(x - 1) + \log(x + 2) = 1 </code></p>
<p>Solve.</p><p> <code class='latex inline'>\log_x5=2</code></p>
<p> Solve the equation.</p><p><code class='latex inline'> \displaystyle \log x^{\log x} =1 </code></p>
<p>Solve for x.</p><p><code class='latex inline'> \displaystyle \log_3x + \log_{\sqrt{x}}x - \log_{\frac{1}{3}}x = 6 </code></p>
<p>Find the roots of each equation. </p><p><code class='latex inline'>6 - 3\log(2n) = 0</code></p>
<p>Solve and leave your answer in exact form.</p><p><code class='latex inline'> \displaystyle 2^{k - 2} = 3^{k + 1} </code></p>
<p>Solve for the unknown.</p><p><code class='latex inline'>2 - \log_4(k - 11) = 0</code></p>
<p> Solve the equation.</p><p><code class='latex inline'> \displaystyle \log x + \log(x - 3) = 1 </code></p>
<p>Solve.</p><p><code class='latex inline'>\displaystyle \log x + \log(x -3) = 1 </code></p>
<p><code class='latex inline'>\displaystyle 5^{2 x}=56 </code></p>
<p>Solve for the unknown.</p><p><code class='latex inline'>\log(k + 2)+ \log(k - 1) = 1</code></p>
<p>Solve each equation.</p><p>a) <code class='latex inline'>\log_5(\log_3x)=0</code></p>
<p>Find the roots of each equation, correct to two decimal places, using graphing technology. Sketch the graphical solution.</p><p><code class='latex inline'> \displaystyle 3\log(x - 2) = \log(2x) -3 </code></p>
<p><code class='latex inline'>\displaystyle 3^{x-1}=72 </code></p>
<p>Solve each equation.</p><p>b) <code class='latex inline'>\log_2(\log_4x)=1</code></p>
<p>Solve and check for extraneous roots. Where necessary, round answers to 2 decimal places.</p><p><code class='latex inline'>\displaystyle 3^{2x} = 7(3^x) - 12 </code></p>
<p>Find the roots of each equation. </p><p><code class='latex inline'>\log(k- 8) = 2</code></p>
<p>Solve for <code class='latex inline'>x</code>, correct to two decimal places. </p><p><code class='latex inline'> x = 10e ^{\dfrac{-3}{2}}</code></p>
<p>Solve for x.</p><p><code class='latex inline'> \displaystyle \log 10^{\log(x^2 + 21)} - 1 = \log x </code></p>
<p>Solve.</p><p><code class='latex inline'>\log_6x-\log_6(x-1)=1</code></p>
<p>Solve each equation. If necessary, round to the nearest ten-thousandth.</p><p><code class='latex inline'>\displaystyle \log (5 x-4)=3 </code></p>
<p>Solve each equation. If necessary, round to the nearest ten-thousandth.</p><p><code class='latex inline'>\displaystyle 9^{2 x}=42 </code></p>
<p>Solve for <code class='latex inline'>x</code>, correct to two decimal places. </p><p><code class='latex inline'> 10 = 100e ^{\dfrac{-x}{4}}</code></p>
<p>Solve and leave your answer in exact form.</p><p><code class='latex inline'> \displaystyle 4^{2x } -4^x - 20 = 0 </code></p>
<p>Reasoning The graphs of <code class='latex inline'>\displaystyle y=2^{3 x} </code> and <code class='latex inline'>\displaystyle y=3^{x+1} </code> intersect at approximately <code class='latex inline'>\displaystyle (1.1201,10.2692) . </code> What is the solution of <code class='latex inline'>\displaystyle 2^{3 x}=3^{x+1} ? </code></p>
<p>Solve each equation. Check your answers.</p><p><code class='latex inline'>\displaystyle \ln \frac{x-1}{2}=4 </code></p>
<p> Determine the coordinates of the point(s) of intersection of the graphs of </p><p> <code class='latex inline'>y = \log_{10}(x -2)</code> and <code class='latex inline'>y = 1- \log_{10}(x + 1)</code>. </p>
<ol> <li>Using the change of base formula, what is the solution of <code class='latex inline'>\displaystyle \log _{5} x=\log _{3} 20 ? </code> Round the answer to the nearest tenth.</li> </ol>
<p>Solve each equation. If necessary, round to the nearest ten-thousandth.</p><p><code class='latex inline'>\displaystyle 8^{x}=444 </code></p>
<p> Solve for x.</p><p><code class='latex inline'>\displaystyle 2(2^{6x}) - 7(2^{4x}) + 7(2^{2x}) - 2 = 0 </code></p>
<p>Solve each equation.</p><p><code class='latex inline'>\displaystyle \log x-\log 3=8 </code></p>
<p>Solve for the unknown.</p><p><code class='latex inline'>1 + \log y = \log(y + 9)</code></p>
<p>Solve. </p><p><code class='latex inline'> \displaystyle \log\sqrt{x^2 + 48x} = 1 </code></p>
<p>Solve and leave your answer in exact form.</p><p><code class='latex inline'> \displaystyle 2^{x } + 12(2)^{-x} = 7 </code></p>
<p>Solve each equation. Check your answers.</p><p><code class='latex inline'>\displaystyle 2 \ln 2 x^{2}=1 </code></p>
<p>Solve the following system of equations algebraically.</p><p><code class='latex inline'>y=\log_2(5x+4)</code></p><p><code class='latex inline'>y=3+\log_2(x-1)</code></p>
<p>Find the roots of each equation. </p><p><code class='latex inline'>1 - \log(w- 7) = 0</code></p>
<p>Solve.</p><p> <code class='latex inline'>\displaystyle{\log_x27=\frac{3}{2}}</code></p>
<p>Evaluate, rounding to three decimal places, if necessary. </p><p>a) <code class='latex inline'>ln(e^{\dfrac{3}{4}})</code></p>
<p>Solve.</p><p> <code class='latex inline'>\log_3x=4\log_33</code></p>
<p>Solve for the unknown.</p><p><code class='latex inline'>\log x^3- \log 2 = \log(2x^2)</code></p>
<p> Solve the equation.</p><p><code class='latex inline'> \displaystyle 100^{\log (x+20)} =10000 </code></p>
<p>The graphs of the equations <code class='latex inline'> y=3 x-20 </code> and <code class='latex inline'> y=-2 x+10 </code> intersect at the point <code class='latex inline'> (6,-2) </code> . Without solving, find the solution of the equation <code class='latex inline'> 3 x-20=-2 x+10 </code> .</p>
<p>Solve each equation. Leave answers in exact form.</p><p><code class='latex inline'>\displaystyle 5^{x-2} = 4^{x } </code></p>
<p>Mental Math Solve each equation.</p><p><code class='latex inline'>\displaystyle \log _{9} 3=x </code></p>
<p>Solve and check for any extraneous roots.</p><p><code class='latex inline'> \displaystyle \frac{2}{3} = \log\sqrt[3]{w^2 - 10w} </code></p>
<p>a) Without solving the equation, state the restrictions on the variable <code class='latex inline'>x</code> in the following: <code class='latex inline'>\log(2x-5)-\log(x-3)=5</code></p><p>b) Why do these restrictions exist?</p>
<p>Solve for <code class='latex inline'>x</code>.</p><p><code class='latex inline'>3^{2x}-12(3^x)+27=0</code></p>
<p>Solve for the unknown.</p><p><code class='latex inline'>log(v - 1) = 2 + \log(v - 16)</code></p>
<p>Solve.</p><p> <code class='latex inline'>\log_28=x</code></p>
<p>Solve. Express each answer to three decimal places.</p><p><code class='latex inline'>\displaystyle 8\cdot 3^x = 132 </code></p>
<p>Solve and leave your answer in exact form.</p><p><code class='latex inline'> \displaystyle 3^{x - 2} = 5^x </code></p>
<p>Solve for the unknown.</p><p><code class='latex inline'>\log x + \log(x - 4) = 1</code></p>
<p> Solve.</p><p><code class='latex inline'>\displaystyle \log_3(8x - 2 + \log_3(x - 1)) =2 </code></p>
<p> Solve the equation.</p><p><code class='latex inline'> \displaystyle x^210^x - x10^x = 2(10^x) </code></p>
<p>Solve.</p><p><code class='latex inline'> \displaystyle \log(2x +10) = 2 </code></p>
<p>Solve each equation. Check your answers.</p><p><code class='latex inline'>\displaystyle \ln 3 x=6 </code></p>
<p>Solve for <code class='latex inline'>t</code>. Round answers to two decimal places.</p><p><code class='latex inline'>\displaystyle 0.5 = 1.2^{t - 1} </code></p>
<p>Solve.</p><p><code class='latex inline'>\displaystyle{\log_{\frac{1}{3}}27=x}</code></p>
<p>Consider the equation <code class='latex inline'>\displaystyle10 = 2^x</code>.</p><p><code class='latex inline'>10 = </code>?</p>
<p>Solve each equation. If necessary, round to the nearest ten-thousandth.</p><p><code class='latex inline'>\displaystyle 4 \log _{3} 2-2 \log _{3} x=1 </code></p>
<p>Solve. </p><p><code class='latex inline'> \displaystyle \log_2(x + 5) - \log_2(2x) = 8 </code></p>
<p>Solve each equation. Check your answers.</p><p><code class='latex inline'>\displaystyle \ln (4 x-1)=36 </code></p>
<p>Solve <code class='latex inline'>3^x = 15</code> by taking the natural logarithm of both sides.</p>
<p> Solve the equation.</p><p><code class='latex inline'> \displaystyle 2^{2/\log_{5}x} = \frac{1}{16} </code></p>
<p><code class='latex inline'>\displaystyle 5^{3 x}=500 </code></p>
<p>Solve each equation.</p><p><code class='latex inline'>\displaystyle 3 \log x-\log 6+\log 2.4=9 </code></p>
<p>Solve for the unknown.</p><p><code class='latex inline'>\log(p+5) - \log(p + 1) =3</code></p>
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