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

Question

3841 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-05-10T11:55:34

$9/8$

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 $loga-logb=log(a/b)$ , so

$log_7 (9/8)=log_7 x$

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

$9/8=x$

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