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

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lkballer24 | Student, Grade 11 | Valedictorian

Posted September 5, 2012 at 3:29 PM via web

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

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted September 5, 2012 at 4:22 PM (Answer #1)

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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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