Question

Find the value of the following: ${\left(\frac{1}{2}\right)}^{{log}_{2}5}$

Answer 1

${\left(\frac{1}{2}\right)}^{{log}_2^5}$
we know,
$\left(\frac{1}{a}\right)=a^{-1}$
also, ${-log}_b^a={log}_b^{\frac{1}{a}}$
$\Rightarrow {\left(\frac{1}{2}\right)}^{lo{g}_2^5}=2^{{log}_2^{1/5}}=\frac{1}{5}$
we know, $a^{{log}_a^b}=b$