Question 112835
First let's start with the basic logarithmic identity:


{{{log(x,ab)=log(x,a)+log(x,b)}}}


Using that, we can say:


{{{log(x,4)+log(x,9)=log(x,4*9)=log(x,36)=2}}}


But we also know that {{{log(x,36)=2}}} is equivalent to saying:


{{{36=x^2}}}


So, taking the square root of both sides, {{{x=6}}}.


Note that -6 which satisfies our equation {{{36=x^2}}}, cannot be a solution because the definition of the logarithm function says that the base must be greater than zero.


Hope this helps.

John