I am given this question and told to solve for $a,b,c$:
$$\frac{y^{8a}x^{b}\log_x(y^{8a})}{2x^2y^c} = \frac{y^{3/2}\ln(y)}{3\ln(x)}$$
I tried to convert all the logarithms to $\ln$ and remove the $\frac{\ln(x)}{\ln(y)}$ term from both sides of the equation, but eventually I am stuck as this expression has 2 variables $x,y$ which are unknowns.
I got a final form $8ay^{8a-c-3/2} = 2x^{2-b}$, thus concluding that $a=1/4$, but from there I do not know how to continue on.
Any help is greatly appreciated. Thanks.