find a & b if a^(a+1) = 16^(b+2) and (1/2)^(3+a)=(1/4)^3b

Asked by  | 30th Apr, 2013, 08:38: PM

Expert Answer:

a^(a+1) = 16^(b+2) (1)
 
 
Also, (1/2)^(3+a)=(1/4)^3b          
i.e.(1/2)^(3+a)=(1/2)^6b    
Comparing powers as the bases are same
3+a = 6b
a = 6b-3
 
Substituting it in the first equation
(6b-3)^(6b-2) = 16^(b+2)
this equation is not satisfied for any value of b
 
Hence, there exists no solution.
 
 
 

Answered by  | 1st May, 2013, 07:20: PM

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