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How to solve this exponential equation:

n*2^n=2^37

n=32

Is my answer correct ?

n*2^n=2^37=>

2^37=2^5*2^32=>

32*2^32=>

n=32

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    please show your efforts... – 2017-02-11
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    @Vikrant Desai , added – 2017-02-11

2 Answers 2

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No its not. You have minor mistake.

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

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

Solution -

$n × 2^n = 2^{37}$

$n × 2^n = 2^5 × 2^{32}$

$n × 2^n = 32 × 2^{32}$

So n = 32.

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    Oops yeah it was a typo , thanks – 2017-02-11
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    If its typo. Your solution and answer is perfect. – 2017-02-11
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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 $$n=32$$