### Home > CCA2 > Chapter Ch11 > Lesson 11.2.2 > Problem11-59

11-59.

Rewrite each equation as an equivalent equation using log$_{10}$. You do not need to find a numerical answer. These are sometimes known as change of base problems.

1. log$_2$$(3) = x$

Write the equation in exponential form.

$2^x = 3$

Take the logarithm of base $10$.

log$_{10}$$(2^x) =$ log$_{10}$$(3)$

Use the Power Property of Logarithms and solve for $x$.

xlog$_{10}$$(2) =$ log$_{10}$$(3)$

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

1. log$_5$$(8) = x$

Use the same process as in part (a).

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

1. log$_7$$(12) = x$

Use the same process as in part (a).

1. log$_a$$(b) = x$

Use the same process as in part (a).