Question

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

Answer 1

Given ${\log }_{10}a=b\Rightarrow (10{)}^b=a$
Now ${10}^{2b-3}=\frac{(10{)}^{2b}}{(10{)}^3}=\frac{{\left({10}^b\right)}^2}{10\times 10\times 10}=\frac{{\left({10}^b\right)}^2}{1000}$
$$=\frac{a^2}{1000}\text{.}$$