Question

Find the value of $x$ if ${\log }_5\sqrt[3]{35}=x$

Answer 1

We know that, ${\log }_{a}b=c⟹b=a^c$

$\therefore {\log }_5\sqrt[3]{35}=x$

$\Rightarrow \sqrt[3]{35}=5^x$

$\Rightarrow 5^{1/3}=5^x$

As the bases are same, equating the powers

$\Rightarrow x=\frac{1}{3}$