Solving Equations using logarithm Here is a system of equations for which I am having difficulty solving:
\begin{cases} a^{2x}.b^{3y}=m^5 \\ a^{3x}.b^{2y}=m^{10} \end{cases}

HINT
Notice that $$a^{2x}.b^{3y}=m^5 \\a^{3x}.b^{2y}=m^{10}$$
$$\Rightarrow a^{3x}.b^{2y}=(a^{2x}.b^{3y})^2$$
Now solve either of for $a$ or $b$. The solution you obtain will be dependent on $m$.
