Question

Find the exact value of x. (25)^(x-20)=((1)/(125))^(x)

Answer 1

x = 8

Explanation:

`{25}^((x - 20)) = \frac{1}{ {125}^(x) } \\ \\ {5}^(2(x - 20)) = \frac{1}{ {5}^(3x) } \\ \\ {5}^(2x - 40) = {5}^( - 3x) \\ \\ 2x - 40 = - 3x ..(bases \: are \: equal \: \\ therefore \: exponents \: will \: also \: be \: equal)\\ 2x + 3x = 40 \\ 5x = 40 \\ x = (40)/(5) \\ \huge \purple{ \boxed{ x = 8}}`