Question 134734
Given: {{{log(x-2)+log(2x-3)=2Logx}}}
{{{10^(log(x-2)+log(2x-3))=10^(2Logx) }}}
{{{10^(log(x-2))*10^(log(2x-3))=10^(2Logx) }}}
{{{(x-2)(2x-3) = x^2 }}}
{{{2x^2 -7x + 6 = x^2}}}
{{{x^2 -7x + 6 = 0}}}
{{{(x -1)(x-6) = 0 }}}
x = 1, 6 are possible solutions

Verify
Does Log(4) + Log(9) = 2*Log(6) ??
Does Log(-1) + Log(-1) = 2*Log(1) --> there is no such thing as a real number with a negative log, so 1 is not an answer.