# What can be the value of $m$ in following equation

During calculations I got this step $$(e^m/((m+1)^{m+1}) )^{3n/4} = 1/2^n$$

I want the value of m here??

• Assuming $n,m\in\Bbb R$ (or some subset), take the $\frac {3n}4$ root of both sides, then see what else makes sense from there... – abiessu Oct 28 '13 at 1:59

Well, you can eliminate $n$ by raising both sides to $4/(3n)$:
$$\frac{e^m}{(m+1)^{m+1}} = \frac{1}{2^{4/3}}.$$
I don't think there's much hope of a closed-form solution, but Wolfram Alpha can easily find $m$ numerically.
Note that more, (likely complex, depending on $n$) solutions also exist -- multiply the right-hand side by $4/(3n)$th roots of unity.