Question 202237
Solve for x:
{{{Log(2x-3) = Log(x)+Log(x-2)}}} Apply the "product rule" for logarithms to the right side of the equation. {{{Log[b](M*N) = Log[b](M)+Log[b](N)}}}
{{{Log(2x-3) = Log((x)*(x-2))}}} Simplify the argument on the right side.
{{{Log(2x-3) = Log(x^2-2x)}}} Apply the "identity" property.:If {{{Log[b](M) = Log[b](N)}}} then {{{M = N}}}
{{{2x-3 = x^2-2x}}} Form into a standard quadratic equation.
{{{x^2-4x+3 = 0}}} Factor.
{{{(x-1)(x-3) = 0}}} Apply the "zero product" rule.
{{{x-1 = 0}}} or {{{x-3 = 0}}} therefore:
{{{highlight(x = 1)}}} or {{{highlight(x = 3)}}}