Question

Given ${\log }_{10}a=m$ and ${\log }_{10}b=n$, express $\frac{a^3}{b^2}$ in terms of $m$ and $n$.

Answer 1

${\log }_{10}a=m\Rightarrow a={10}^m$

${\log }_{10}b=n\Rightarrow b={10}^n$

$\frac{a^3}{b^2}=\frac{{\left({10}^m\right)}^3}{{\left({10}^n\right)}^2}$

$=\frac{\left({10}^{3m}\right)}{\left({10}^{2n}\right)}$

$={10}^{3m-2n}$