Question 236505
Solve for x:
{{{log((x-1))-log((x+6)) = log((x-2))-log((x-3))}}} Apply the quotient rule for logarithms:{{{log((M))-log((N)) = log((M/N))}}}
{{{log(((x-1)/(x+6))) = log(((x-2)/(x-3)))}}} If {{{log((M)) = log((N))}}} then {{{M = N}}}
{{{(x-1)/(x+6) = (x-2)/(x-3)}}} Cross-multiply.
{{{(x-1)(x-3) = (x-2)(x+6)}}} Perform the indicated multiplication.
{{{x^2-4x+3 = x^2+4x-12}}} Subtract {{{x^2}}} from both sides.
{{{-4x+3 = 4x-12}}} Add 4x to both sides.
{{{3 = 8x-12}}} Add 12 to both sides.
{{{15 = 8x}}} Divide both sides by 8.
{{{x = 15/8}}} 
{{{highlight(x = 1.875)}}}