Question 613455
Combine using the product rule of logarithms.
{{{log((x+21)(x))=2}}}

<p>Let both sides have a base of 10. 
{{{10^(log(x(x+21)))=10^(2)}}}

<p>Remember that log is assumed to be 10 if there's no number specified. Because we made the equation have a base of 10, we can then cancel out the logs.
{{{x(x+21)=10^(2)}}}

<p>Multiply x by each term inside the parentheses.
{{{x^(2)+21x=10^(2)}}}

<p>Square 10. 
{{{x^(2)+21x=100}}}

<p>Move 100 to the other side.
{{{x^(2)+21x-100=0}}}

<p>Factor. 
*[invoke factoring_quadratics 1, 21, -100]

<p><p>Set each of the factors equal to 0.
{{{x+25=0}}},{{{x-4=0}}}

<p>Simplify.
{{{x=-25}}},{{{x=4}}}

<p>Here is the final answer:
<b>x=-25,4</b>

<p>:)