Question 186597
In general:
{{{log(a) - log(b) = log(a/b)}}}
and 
{{{a*log(b) = log(a^b)}}} 
{{{2ln(2) - ln(x-1) = ln(2x)}}}
{{{ln(2^2) - ln(x-1) = ln(2x)}}}
{{{ln(4/(x-1)) = ln(2x)}}}
{{{4/(x-1) = 2x}}}
{{{4 = 2x*(x-1)}}}
{{{4 = 2x^2 - 2x}}}
{{{2x^2 - 2x - 4 = 0}}}
{{{x^2 - x - 2 = 0}}}
{{{(x - 2)(x + 1) = 0}}}
{{{x = 2}}}
{{{x = -1}}}
check:
{{{2ln(2) - ln(x-1) = ln(2x)}}}
{{{2ln(2) - ln(2-1) = ln(2*2)}}}
{{{ln(4) - ln(1) = ln(4)}}}
{{{ln(4) - 0 = ln(4)}}}
OK
{{{2ln(2) - ln(x-1) = ln(2x)}}}
{{{2ln(2) - ln(-1-1) = ln(2*(-1))}}}
The negative root doesn't work since
raising {{{e}}} to a power can't 
result in a negative