Log(3x)3=log(x^2)3

Question

Log(3x)3=log(x^2)3

anonymous · Answer

x=3

anonymous · Answer

Yea , really hard to figure out . Actually i was hoping for a solution .

turingtest · Answer

Is it log(3x)(3) on the left side?
or [log(3x)]^3 ?

anonymous · Answer

It is log(3x)(3)

turingtest · Answer

ok,then that is the same as$$3 \log (3x)=3\log(x^2)$$using log properties:$$\log(27x^3)=\log(x^6)$$raise ten to both sides:$$27x^3=x^6\rightarrow27=x^3$$$$x=\sqrt[3]{27}=3$$if you didn't follow me tell me where you got lost :)

anonymous · Answer

Did you solve these with logarithm base 10  or with bases (3x) and (x^2) ?

turingtest · Answer

I assumed they were base ten logs, but it doesn't matter because if they were base 2 or 50 they would still cancel.
if we had
log(x)=y
then we need to know what the base is (call it n), because after raising both sides to that power we get
x=n^y
but as long as it's
log(x)=log(y)
regardless what the base is we can infer
x=y

PS I have never seen a log with an x^2 base, so don't expect one anytime soon.