Question 170256
Solve for x:
{{{Log[2](x+5) + Log[2](x-1) = 4}}} Apply the "product rule" ({{{Log[b](M)+Log[b](N) = Log[b](M*N)}}}) for logarithms to the left side.
{{{Log[2]((x+5)(x-1)) = 4}}} Simplify the argument on the left side.
{{{Log[2](x^2+4x-5) = 4}}} Rewrite the left side in its exponential form:({{{Log[b](x) = y}}} means {{{b^y = x}}})
{{{2^4 = x^2+4x-5}}} Simplify.
{{{x^2+4x-5 = 16}}} Subtract 16 from both sides.
{{{x^2+4x-21 = 0}}} Factor this quadratic equation.
{{{(x-3)(x+7) = 0}}} Apply the zero product rule: If A*B = 0, then either A = 0, or B = 0, or both.
{{{x-3 = 0}}} or {{{x+7 = 0}}} so that...
{{{x = 3}}} or {{{x = -7}}}