Question

solve 2^ log 15 to the base 2 root 2

Answer 1

${2}^{ log_{2 \sqrt{2} }(15) }$

${2}^{ log_{ {2}^{ \frac{3}{2} } }(15) }$

As,

$log_{ {a}^{k} }(b) = \frac{ log_{a}(b) }{k}$

and

${a}^{ log_{b}(c) } = {c}^{ log_{b}(a) }$

$\implies {2}^{ log_{2 \sqrt{2} }(15) } = 15 ^{ \frac{2}{3} } = \sqrt[3]{225}$

$\implies {2}^{ log_{2 \sqrt{2} }(15) } \approx6.0822...$