# How do you simplify 7^ (log _(7)9 - log_(7)8)?

May 10, 2016

$\frac{9}{8}$

#### Explanation:

Say that this equation equals $x$, so

${7}^{{\log}_{7} 9 - {\log}_{7} 8} = x$

Now take the ${\log}_{7}$ of both sides to get rid of the powers,

${\log}_{7} 9 - {\log}_{7} 8 = {\log}_{7} x$.

We know that $\log a - \log b = \log \left(\frac{a}{b}\right)$, so

${\log}_{7} \left(\frac{9}{8}\right) = {\log}_{7} x$

Raise both sides by the base of $7$ to remove logarithms, and find the answer

$\frac{9}{8} = x$