How do you solve \log _ { 3} 9^ { x } = 10?

2 Answers
Oct 15, 2017

x=5

Explanation:

Using the rule log_aM=N rArr M=a^N you can rewrite the equation as 9^x=3^10

9^x=59 049
Log both sides to bring x down so you can solve for it.
log 9^x=log59049
x=log59049/log9
x=5

Oct 15, 2017

The answer is 5. See explanation.

Explanation:

log_3 9^x=10

First I use the rule:

log_a b^c=c*log_a b

After using this rule I get:

x*log_3 9=10

log_3 9=2, so we get:

2x=10 => x=5