# An algebra problem by Aira Thalca

Algebra Level 4

$\large 25^x = 10^x + 4^{x+1}$

The solution $$x$$ of the equation above can be written as $$\log_{\frac{a}{b}}\left(\frac{c+\sqrt{d}}e\right)$$, where $$a$$, $$b$$, $$c$$, $$d$$ and $$e$$ are positive integers with $$a$$ and $$b$$ being relatively primes and $$d$$ square-free.

Find the value of the product $$abcde$$.

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