Question

If $a={\log }_{10}x$, find the following in terms of a:
(i) $x$
(ii) ${\log }_{10}\sqrt[5]{5x^2}$

Answer 1

$a={\log }_{10}x$

$\left(i\right)\Rightarrow x={10}^a$

Substituting $x={10}^a$ in ${\log }_{10}{x}^{\frac{2}{5}}$

$\left(ii\right){\log }_{10}{\left({10}^a\right)}^{\frac{2}{5}}$

$={\log }_{10}{10}^{\frac{2a}{5}}$

$=\frac{2a}{5}{\log }_{10}10$

$=\frac{2a}{5}$ since ${\log }_{10}10=1$