solve the equation by expressing each side as a power of the same base and then equating exponents

Question

3125^x=1/square root 5

Answer 1

did you realize that 3125 is a power of 5, namely 3125 = 5^5

and √5 = 5^(1/2) then 1/√5 = 5^(-1/2)

so your equation becomes
(5^5)^x = 5^(-1/2)
5^5x = 5^(-1/2)
then 5x = -1/2
x = -1/10