Question 374141
{{{ln(x-2) - lnx = 4}}},
{{{ln((x-2)/x) = 4}}},
{{{(x-2)/x = e^4}}}, the equivalent exponential equation.
{{{x-2 = e^4*x}}},after cross-multiplication.
{{{x - e^4*x = 2}}},
{{{x(1-e^4) = 2}}},
{{{x =2/ (1-e^4)}}}.
This is approximately equal to -0.0373.  Since this value won't satisfy the original equation, we discard this value, and conclude the equation has an empty solution set.