If {({a^m})^n} = {a^{{m^n}}} , then value of 'm' in terms of 'n' is

English

Gujarati

Hindi

Basic of Logarithms

easy

If ${({a^m})^n} = {a^{{m^n}}}$, then the value of $'m'$ in terms of $'n'$ is

A

$n$

B

${n^{1/m}}$

C

${n^{1/(n - 1)}}$

D

None of these

Solution

(c) ${({a^m})^n} = {a^{{m^n}}} = {a^{mn}} \Rightarrow mn = {m^n}$

$ \Rightarrow $$n = {m^{n – 1}} \Rightarrow m = {n^{{1 \over {n – 1}}}}$.

Standard 11

Mathematics

Share

Similar Questions

$\root 4 \of {(17 + 12\sqrt 2 )} = $

medium

The greatest number among $\root 3 \of 9 ,\root 4 \of {11} ,\root 6 \of {17} $ is

medium

${{\sqrt 2 } \over {\sqrt {(2 + \sqrt 3 )} – \sqrt {(2 – \sqrt 3 } )}} = $

easy

Solution of the equation ${4.9^{x – 1}} = 3\sqrt {({2^{2x + 1}})} $ has the solution

medium

$\sqrt {(3 + \sqrt 5 )} – \sqrt {(2 + \sqrt 3 )} = $

medium