Question 382936
Solve for x:
{{{Log(x)+Log(x+21) = 2}}} Apply the product rule:
{{{Log((x)(x+21)) = 2}}} Simplify the argument.
{{{Log(x^2+21x) = 2}}} Rewrite this in exponential form.
{{{10^2 = x^2+21x}}} Rewrite as a quadratic equation in standard form.
{{{x^2+21x-100 = 0}}} Factor.
{{{(x-4)(x+25) = 0}}} Apply the zero product rule.
{{{(x-4) = 0}}} or {{{x+25 = 0}}} so...
{{{x = 4}}} or {{{x = -25}}} Discard the negative solution as the log of a negative number is not real.
{{{x = 4}}}
Check:
{{{Log(4)+Log(4+21) = Log(4)+Log(25)}}}={{{2}}}