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AoPS Wiki:Problem of the Day/September 16, 2011

When the equation \[13^3x+13^x=10\] is solved for $x$, the result is $x=\log_{a}b$, where $a$ and $b$ are positive integers and $a$ is not a multiple perfect power other than $1$. Find $(a+b)(a^2-ab+b^2)$.

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