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?
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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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$$11 \cdot 16^{1/(n-1)} = 16^{n/(n-1)} - 10$$ $$11 \cdot 16^{1/(n-1)} = 16^{1+1/(n-1)} - 10$$ $$11 \cdot 16^{1/(n-1)} = 16\cdot16^{1/(n-1)} - 10$$ $$16\cdot 16^{1/(n-1)} - 11\cdot16^{1/(n-1)}=10$$ $$5\cdot 16^{1/(n-1)}=10$$ $$16^{1/(n-1)}=2=16^{1/4}$$ $$1/(n-1)=1/4$$ $$n=5$$ |
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