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Garrett Black 2022-06-28 Answered
Solve a = x n   ,   b = ( x + 1 ) n for x , n
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Answers (1)

candelo6a
Answered 2022-06-29 Author has 24 answers
b a = ( x + 1 x ) n
( b a ) 1 n = 1 + 1 x
x = 1 ( b a ) 1 n 1
Substitute this in ( 1 ) to find n.
Now use since x is an integer and given x = 1 ( b a ) 1 n 1 , what can you infer?
EDIT: As x is a positive integer as is said by OP in the comments, hence ( b a ) 1 n 1 = 1, or b = a 2 n or n = l o g b a l o g 2 .
n = l o g b a l o g 2 and x = 1
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