Indices problem

Algebra Level 2

$\large 2^m=3^n$

Can the above statement ever be true? If yes, for what value of $n$ ?

n=0.63093074m n=0.6309297537m Can never be true n=1.63m

1 solution

Sir isaac Newton
Nov 10, 2017

$2^m=3^n$
$mlog(2)=nlog(3)$
$\frac{n}{m}=\frac{log(2)}{log(3)}$
$n=0.6309297537m$