Question

If ${\log }_{l}n=2$ & ${\log }_{n}2l=2$, find $l^3=$?

Answer 1

Given,

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

or, $n=l^2$.....(1) [ From the definition of logarithm]

And ${\log }_{n}2l=2$

or, $2l=n^2$......(2).

Now multiplying both sides of (2) with $l^2$ we get,

$2l^3=n^2{l}^2$

or, $2l^3=n^2.n$[ Using (1)]

or, $l^3=\frac{n^3}{2}$.