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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.

 Aug 4, 2022
 #1
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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

 

 

cool cool cool

 Aug 4, 2022

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