If $g(x)=\sqrt[3]{\frac{x+3}{4}}$, for what value of $x$ will $g(2x)=2(g(x))$? Express your answer in simplest form.

Interesting problem. I will denote the cube root of something as cbrt. Then you have cbrt((2x+3)/4)=2cbrt((x+3)/4). Now just cube both sides and you have an easy linear equation. The solution is x=-7/2, your answer.