Question

solve the equation log[1/3](x^2+x)-log[1/3](x^2-x)=-2

Answer 1

first of all, you would have to know that
\[\log_ax-\log_ay = \log_a \frac{ x }{ y }\]

Answer 2

\[\log _{_{\frac{ 1 }{ 3 }}}x^2+x-\log _{\frac{ 1 }{ 3 }}x^2-x=-2\]
\[\log _{\frac{ 1 }{ 3 }}\frac{ x^2+x }{ x^2-x }=-2\]

Answer 3

using the fact that
\[\log_ax=b\] is the same as writing
\[a^b=x\]