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}

Taking the logarithms of both these equations will yield a linear system in $x,y$:
$$\begin{cases}2\log(a)x+3\log(b)y=5\log(m)\\3\log(a)x+2\log(b)y=10\log(m)\end{cases}.$$
About solving linear systems, maybe this helps: https://www.mathplanet.com/education/algebra-1/systems-of-linear-equations-and-inequalities/the-substitution-method-for-solving-linear-systems .
