Question

3^log 9x=2

Answer 1

\[3^{\log_{9} x} =2\]

Answer 2

We have
\[\huge 3^{\log_9 x}=2\]
We know
\[\log_b c= \frac{\log_a c}{\log_a b}\]
so let's write
\[\log_9 x=\frac{\log_3 x}{\log_3 9}\]
do you know what's the value of \(\log_3 9 \) ?

Answer 3

I think you can use this too,
\[a^b=c~~,~~\log_{a}c=b\]

Answer 4

@gF did you understand ???

Answer 5

We have
3log9x=2
We know
logbc=logaclogab
so let's write
log9x=log3xlog39
do you know what's the value of log39 ?