7.030. $x \lg \sqrt[5]{5^{2 x-8}}-\lg 25=0$.

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7.030. $x \lg \sqrt[5]{5^{2 x-8}}-\lg 25=0$.
## Solution.

$x \lg 5^{\frac{2 x-8}{5}}=\lg 25, \lg 5^{\frac{(2 x-8) x}{5}}=\lg 5^{2}, 5^{\frac{2 x^{2}-8 x}{5}}=5^{2}$,

$\frac{2 x^{2}-8 x}{5}=2, x^{2}-4 x-5=0$,

from which $x_{1}=5, x_{2}=-1$.

Answer: $5; -1$.