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

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Answer 1 · 2017-10-15T14:58:10

#x=5#

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#

Answer 2 · 2017-10-15T15:09:57

The answer is #5#. See explanation.

#log_3 9^x=10#

First I use the rule:

After using this rule I get:

#log_3 9=2#, so we get: