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

1 Answer
May 10, 2016

Answer:

#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 #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#