What is the value of b if 5^b + 5^b + 5^b + 5^b + 5^b = 625^(b - 1)? Express your answer as a common fraction.
The left side of the expression evaluates to
5*5^b = 5^(b + 1)
and
625 = 5^4
So....
5^(b + 1) = (5^4)^(b - 1)
5^(b + 1) = 5^(4b - 4)
Equating bexponents
b + 1 = 4b - 4
5 = 3b
b = 5 / 3
