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I am stuck on this problem. Find the value of $x$ in this expression:

$$ \ln(x-2) \cdot \ln(x)=\ln(64) $$

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    Why do you expect this to be solvable...? Or are numerical methods reasonable? – 2017-01-25
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    Maybe it's addition instead of multiply – 2017-01-25

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Little bit of algebra that is not interesting gives $(x-2)^{\log{x}}=64$ or $x^{\log{x-2}}=64$. RHS is strictly increasing in $x$, equals $1$ at $x=3$ and is larger than $70$ at $x=9$. Hence the unique solution is in $[3,9]$. Numerically, it is approximately $8.78151$.