# So Many Logs!

Algebra Level 4

$\large { 6 }^{ \log _{ 5 }{ x } }\log _{ 3 }( { x }^{ 5 } ) -{ 5 }^{ \log _{ 6 }{ 6x } }\log _{ 3 }{ \left( \dfrac { x }{ 3 }\right) } ={ 6 }^{ \log _{ 5 }{ 5x } }-{ 5 }^{ \log _{ 6 }{ x } }$

If the sum of the solutions to the equation above is equal to $\large { a }^{ \frac { b }{ c } }+d,$

where $a, b, c$ and $d$ are all positive integers with $b$ and $c$ are coprime, what is the smallest possible value of $abc+d$?

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