SOLUTION: Hopefully I've submitted this in the right place to transform a logarithmic expression. Express log x 4/9 in terms of log x 3/2 I worked it out through guesswork as, -2 log

Question 177444: Hopefully I've submitted this in the right place to transform a logarithmic expression.
Express log x 4/9 in terms of log x 3/2
I worked it out through guesswork as, -2 log x 3/2, but can anyone explain the answer and if this is correct.
Thanks
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Express log(base x) 4/9 in terms of log(base x) 3/2
-------------------
log(basex) 4/9
= log(basex) (2/3)^2
= log(basex) (3/2)^(-2)
= -2log(basex) (3/2)
===========================
Cheers,
Stan H.

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
I think you mean expressed in terms of

Your answer is correct. Here's why:

For any non-zero , , and for any non-zero , , and , so that means we can say:

For any , , ,

Now we can say: , presuming

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