Question 21525
Solve for x:
{{{log((x+9)) = 1 - logx}}} Add logx to both sides.
{{{log((x+9)) + logx = 1}}} Simplify the left side. (loga+logb = log(ab))
{{{log((x^2+9x)) = 1}}} Substitute log10 = 1
{{{log((x^2+9x)) = log10}}} If loga = logb then a = b.
{{{x^2+9x = 10}}} Subtract 10 from both sides.
{{{x^2+9x-10 = 0}}} Solve by factoring.
{{{(x-1)(x+10) = 0}}} Apply the zero product principle.
{{{(x-1) = 0}}} and/or {{{(x+10) = 0}}}
If {{{x-1 = 0}}} then, {{{x = 1}}}
If {{{x+10 = 0}}} then, {{{x = -10}}}

You can check the solutions by substitution.