Question

ln(x-2)+ln(2x-3)=2lnx

Help please.

Answer 1

\[\ln(x-2) + \ln(2x-3) = 2\ln x\]
Adding logs is same as taking the log of the product, so:
\[\ln((x-2)(2x-3)) = 2\ln x\]Take anti-log of both sides
\[(x-2)(2x-3) = x^2\]

Now solve that for \(x\). You'll get two solutions, one of which is extraneous because it implies logarithms of negative numbers...

Answer 2

Thank you!

Answer 3

What did you get for an answer?