Question

Using the subsitution y = log(base 3) x, solve the below equation

Answer 1

\[\log_{3} x + 2 = 3 \log_{x}3\]

Answer 2

you can start by converting the log to base 10 by going log(x)/log(3) and the other one to log(3)/log(x)

Answer 3

from there all u have to do is isolate for x. can u do that?

Answer 4

Ok, I have the answer
thanks for your help

Answer 5

I wouldn't do that if I were you... just this use this property
\[\huge \log_b a = \frac1{\log_a b}\]

Answer 6

So that the equation just becomes
\[\huge \log_3x+2=\frac3{\log_3 x}\]
Now substitute the y, as instructed
\[\huge y + 2 = \frac3y\]And isn't that much better? :)