Question

If ${\log }_{8}m=3.5$ and ${\log }_{2}n=7$, then find the value of m in terms of n.

Answer 1

Given,

${\log }_{8}m=3.5$

${\log }_{2}n=7$

$⟹m=8^{3.5}andn=2^7$

$m=8^{35/10}$

$m=(2^3{)}^{7/2}$

$m=(2^7{)}^{3/2}$

$m=n^{3/2}$

$m=n\sqrt{n}$