Solve.
\log_2x=2\log_25
Solve.
\log_3x=4\log_33
Solve.
\log x=3\log2
Solve.
\log(x-5)=\log10
Solve.
\log_28=x
Solve.
\displaystyle{\log_2x=\frac{1}{2}\log_23}
Solve.
\log_x625=4
Solve.
\displaystyle{\log_x6=-\frac{1}{2} }
Solve.
\log_5(2x-1)=2
Solve.
\log(5x-2)=3
Solve.
\log_x0.04=-2
Solve.
\log_5(2x-4)=\log_536
Given the formula from Example 1 for the magnitude of an earthquake, \displaystyle{R=\log\left(\frac{a}{T}\right)+B}, determine the value of a if R=6.3, and T=1.6
Solve.
\displaystyle{\log_x27=\frac{3}{2}}
Solve.
\log_x5=2
Solve.
\log_3(3x+2)=3
Solve.
\log x=4
Solve.
\displaystyle{\log_{\frac{1}{3}}27=x}
Solve.
\displaystyle{\log_{\frac{1}{2}}x=-2}
Solve.
\log_2x+\log_23=3
Solve.
\log3+\log x=1
Solve.
\displaystyle{\log_52x+\frac{1}{2}\log_59=2}
Solve.
d) \log_4x-\log_42=2
Solve.
e) 3\log x-\log3=2\log3
Solve.
\log_34x+\log_35-\log_32=4
Solve \log_6x+\log_6(x-5)=2. Check for inadmissible roots.
Solve.
\log_7(x+1)+\log_7(x-5)=1
Solve.
\log(x-2)+\log_3x=1
Solve.
\log_6x-\log_6(x-1)=1
Solve.
\log(2x+1)+\log(x-1)=\log9
Solve.
\log(x+2)+\log(x-1)=1
Solve.
3\log_2x-\log_2x=8
Describe the strategy that you would use to solve each of the following equations. (Do not solve.)
\log_9x=\log_94+\log_95
Describe the strategy that you would use to solve each of the following equations. (Do not solve.)
\log x-\log2=3
Describe the strategy that you would use to solve each of the following equations. (Do not solve.)
\log x=2\log8
Solve \log_a(x+2)+\log_a(x-1)=\log_a(8-2x).
Solve \log_5(x-1)+\log_5(x-2)-\log_5(x+6)=0.
Explain why there are no solutions to the equations \log_3(-8)=x and \log_{-3}9=x.
a) Without solving the equation, state the restrictions on the variable x in the following: \log(2x-5)-\log(x-3)=5
b) Why do these restrictions exist?
If \displaystyle{\log\left(\frac{x+y}{5}\right)=\frac{1}{2}(\log x+\log y)}, where x>0, y>0, show that x^2+y^2=23xy
Solve \displaystyle{\frac{\log(35-x^3)}{\log(5-x)}=3}.
Given \log_2a+\log_2b=4, calculate all the possible integer values of a and b. Explain your reasoning.
Solve the following system of equations algebraically.
y=\log_2(5x+4)
y=3+\log_2(x-1)
Solve each equation.
a) \log_5(\log_3x)=0
Solve each equation.
b) \log_2(\log_4x)=1
If \displaystyle{\left(\frac{1}{2}\right)^{x+y}=16} and \log_{x-y}8=-3, calculate the values of x and y.