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This is probably an easy task for the users here, but I could not solve it.

$ 11 \cdot 16^{1/(n-1)} = 16^{n/(n-1)} - 10 $

Wolfram Alpha gives the result $ n= 5 $.

What are the steps to solve this?

2 Answers 2

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$11\times 16^{\frac{1}{n-1}}=16^{1+\frac{1}{n-1}}-10=16\times 16^{\frac{1}{n-1}}-10$, so $5\times 16^{\frac{1}{n-1}}=10$, so $16^{\frac{1}{n-1}}=2$, so $\frac{1}{n-1}=\frac{1}{4}$, so $n=5$.

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    Thank you for helping me. I will mark your answer as accepted as soon as possible.2012-12-12
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$11 \cdot 16^{1/(n-1)} = 16^{n/(n-1)} - 10$ $11 \cdot 16^{1/(n-1)} = 16^{1+1/(n-1)} - 10$

$11 \cdot 16^{1/(n-1)} = 16\cdot16^{1/(n-1)} - 10$

$16\cdot 16^{1/(n-1)} - 11\cdot16^{1/(n-1)}=10$

$5\cdot 16^{1/(n-1)}=10$

$16^{1/(n-1)}=2=16^{1/4}$ $1/(n-1)=1/4$ $n=5$