8.6 Solving Logarithmic Equations
Chapter
Chapter 8
Section
8.6
Solutions 46 Videos

Solve.

\log_2x=2\log_25

0.32mins
Q1a

Solve.

\log_3x=4\log_33

0.28mins
Q1b

Solve.

\log x=3\log2

0.18mins
Q1c

Solve.

\log(x-5)=\log10

0.12mins
Q1d

Solve.

\log_28=x

0.16mins
Q1e

Solve.

\displaystyle{\log_2x=\frac{1}{2}\log_23}

0.23mins
Q1f

Solve.

\log_x625=4

0.35mins
Q2a

Solve.

\displaystyle{\log_x6=-\frac{1}{2} }

0.27mins
Q2b

Solve.

\log_5(2x-1)=2

0.13mins
Q2c

Solve.

\log(5x-2)=3

0.17mins
Q2d

Solve.

\log_x0.04=-2

0.26mins
Q2e

Solve.

\log_5(2x-4)=\log_536

0.16mins
Q2f

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

0.54mins
Q3

Solve.

\displaystyle{\log_x27=\frac{3}{2}}

0.33mins
Q4a

Solve.

\log_x5=2

0.18mins
Q4b

Solve.

\log_3(3x+2)=3

0.19mins
Q4c

Solve.

\log x=4

0.12mins
Q4d

Solve.

\displaystyle{\log_{\frac{1}{3}}27=x}

0.24mins
Q4e

Solve.

\displaystyle{\log_{\frac{1}{2}}x=-2}

0.19mins
Q4f

Solve.

\log_2x+\log_23=3

0.23mins
Q5a

Solve.

\log3+\log x=1

0.19mins
Q5b

Solve.

\displaystyle{\log_52x+\frac{1}{2}\log_59=2}

0.42mins
Q5c

Solve.

d) \log_4x-\log_42=2

0.19mins
Q5d

Solve.

e) 3\log x-\log3=2\log3

0.45mins
Q5e

Solve.

\log_34x+\log_35-\log_32=4

0.26mins
Q5f

Solve \log_6x+\log_6(x-5)=2. Check for inadmissible roots.

0.52mins
Q6

Solve.

\log_7(x+1)+\log_7(x-5)=1

0.49mins
Q7a

Solve.

\log(x-2)+\log_3x=1

0.31mins
Q7b

Solve.

\log_6x-\log_6(x-1)=1

0.38mins
Q7c

Solve.

\log(2x+1)+\log(x-1)=\log9

0.56mins
Q7d

Solve.

\log(x+2)+\log(x-1)=1

0.47mins
Q7e

Solve.

3\log_2x-\log_2x=8

0.55mins
Q7f

Describe the strategy that you would use to solve each of the following equations. (Do not solve.)

\log_9x=\log_94+\log_95

0.20mins
Q8a

Describe the strategy that you would use to solve each of the following equations. (Do not solve.)

\log x-\log2=3

0.24mins
Q8b

Describe the strategy that you would use to solve each of the following equations. (Do not solve.)

\log x=2\log8

0.22mins
Q8c

Solve \log_a(x+2)+\log_a(x-1)=\log_a(8-2x).

1.18mins
Q10

Solve \log_5(x-1)+\log_5(x-2)-\log_5(x+6)=0.

1.49mins
Q12

Explain why there are no solutions to the equations \log_3(-8)=x and \log_{-3}9=x.

1.02mins
Q13

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?

0.47mins
Q14

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

1.18mins
Q15

Solve \displaystyle{\frac{\log(35-x^3)}{\log(5-x)}=3}.

3.59mins
Q16

Given \log_2a+\log_2b=4, calculate all the possible integer values of a and b. Explain your reasoning.

1.06mins
Q17

Solve the following system of equations algebraically.

y=\log_2(5x+4)

y=3+\log_2(x-1)

1.39mins
Q18

Solve each equation.

a) \log_5(\log_3x)=0

0.20mins
Q19a

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.