Question

Solve the equation below for x:

log2x + log(2x-1) = log3x

x = 5/4

x = 5/2

x = 0,5/4

There are no solutions.

Answer 1

Make use of the following identities:
log(A) + log(B) = log(AB)
If log(X) = log(Y) then X = Y

Answer 2

log2x + log(2x-1) = log(3x)
log{ 2x(2x-1) } = log(3x)
2x(2x-1) = 3x
4x^2 - 2x - 3x = 0
4x^2 - 5x = 0
x(4x-5) = 0
x = 0 or x = 5/4
x = 0 is not allowed because log(0) is undefined.

So x = 5/4