Solve. Enter any fraction as a simplified fraction. (5√(5))^(-2x+1) = (1)/(5) * 125^(x-3)

Question

Solve.

Enter any fraction as a simplified fraction.


`(5√(5))^(-2x+1) = (1)/(5) * 125^(x-3)`

Answer 1

Explanation:

(5√5)^(1-2x) = 1/5 * 125^(x-3)

(5^1.5)^(1-2x) = 5^(-1) * 125^x / 125^3

5^1.5 / 5^3x = 5^(-1) * 5^(3x) / 5^9

5^1.5 / 5^3x = 5^(3x) * 5^(-10)

5^(1.5 - 3x) = 5^(3x - 10)

=> 1.5 - 3x = 3x - 10

=> 6x = 11.5

=> x = 23/12.