What is the exact solution for `(1/25)*(125)^(x + 2) = root(3)(5^x)`

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The solution for `(1/25)*(125)^(x + 2) = root(3)(5^x)` has to be determined.

`(1/25)*(125)^(x + 2) = root(3)(5^x)`

=> `(1/25)*125^x*(125^2) = 5^(x/3)`

=> `(1/5^2)*5^6*5^(3x) = 5^(x/3)`

=> `5^4*5^(3x) = 5^(x/3)`

=> `5^(4 + 3x) = 5^(x/3)`

As the base is the same equate the exponents

=> `4 + 3x = x/3`

=> `12 + 9x = x`

=> 12 = -8x

=> x = -1.5

**The solution of the equation is x = -1.5**

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