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#