how to solve log x / log 2x = 2

Question

how i can solve this??

Log 2x - Log 2/ Log x + Log 2 = 2

Answer 1

I read this as (log(2x)-log(2))/(log(x)+log(2))=2;

log(2x/2)/log(2x)=2; log(x)/log(2x)=2, which is the title of the question. So far, so good!

log(x)=2log(2x)=log((2x)^2), therefore x=4x^2 and x(4x-1)=0. Since x cannot be zero (because log(x) would be undefined), x=1/4.

CHECK: (log(1/2)-log(2))/(log(1/4)+log(2))=log(1/4)/log(1/2)=-log(2^2)/-log(2)=2log(2)/log(2)=2.