What is the value of b if $5^b + 5^b + 5^b + 5^b + 5^b = 625^{(b-1)}*25^{b}$ ? Express your answer as a common fraction.
+23246 5b + 5b + 5b + 5b + 5b = 625b - 1 · 25b
Left-hand side: 5b + 5b + 5b + 5b + 5b = 5 · 5b = 5b + 1
Right-hand side: 625b - 1 = (54)b - 1 = 54b - 4
25b = (52)b = 52b
--> 625b - 1 · 25b = 54b - 4 · 52b = 56b - 4
Setting the left-had side equal to the right-hand side: 5b + 1 = 56b - 4
This means that: b + 1 = 6b - 4 ---> 5 = 5b ---> b = 1
