# Log!

Algebra Level 3

For what positive integer value of $$x$$ is the $$9^\text{th}$$ term in the expression $$\left( 3^{\log_3 \sqrt{25^{x-1} + 7}} + 3^{-\frac18 \log_3 \left(5^{x-1} + 1\right)} \right)^{10}$$ is 180?

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