How to solve this exponential equation with the given $n$?

Question

How to solve this exponential equation:

$$n2^n=2^{37}\ ?$$

My answer is $n=32$. Is my answer correct? \begin{align} n2^n &= 2^{37} \\ \implies 2^{37} &= 2^5 2^{32} = 32 \cdot 2^{32} \\ \implies n &= 32 \end{align}

Answer 1

No, it’s not. You have a minor mistake.

$2^{37} = 2^5 \cdot 2^{32}$

Not $2^5 + 2^{32}.$

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Solution -

\begin{align} n \times 2^n &= 2^{37} \\ n \times 2^n &= 2^5 \times 2^{32} \\ n \times 2^n &= 32 \times 2^{32}. \end{align} So $n = 32$.

Answer 2

We have $$n\cdot 2^n=2^{37}.$$ Write your equation in the form $$n\cdot 2^n=2^{32}\cdot 2^5$$ and from here we get your solution $$n=32.$$