### Home > A2C > Chapter 11 > Lesson 11.3.2 > Problem11-147

11-147.

Rewrite each equation as an equivalent equation using log10. You do not need to find a numerical answer. These are sometimes known as change of base problems.

1. $\operatorname{log}_{2}\left(3\right) = x$

Write the equation in exponential form.

2x = 3

Take the logarithm of base 10.

log10(2x) = log10(3)

Use the Power Property of Logarithms and solve for x.

xlog10(2) = log10(3)

$x= \frac{ \log_{10}(3) }{\log_{10}(2) }$

1. $\operatorname{log}_{5}\left(8\right) = x$

Use the same process as in part (a).

$x= \frac{ \log_{10}(8) }{ \log_{10}(5)}$

1. $\operatorname{log}_{7}\left(12\right) = x$

Use the same process as in part (a).

1. $\operatorname{log}_{a}\left(b\right) = x$

Use the same process as in part (a).