If a^x = b^y = ab, then find the value of y

Question

If  a^x=b^y=ab , then find the value of y

A.  \frac{(x-1)}{x}

B.  \frac{x}{(x+1)}

C.  \frac{x}{(x-1)}

D.  \frac{x}{(1-x)}

E. x

neha283 · Answer

a^{x} = ab 
 a^{(x-1)} = b  --  (1)

Similarly,  b^{(y-1)} = a  --  (2) 
Replacing  (2)  in  (1)

b^{((y-1)*(x-1))} = b

(y-1) = \frac{1}{(x-1)}

y= \frac{x}{(x-1)}

Option C

napolean92728 · Answer

I multiplied  a^x  and  b^y  to get  (a^x)*(b^y) = ab * ab = (a^2)*(b^2)  and hence  x = 2  and  y = 2  , therefore  x = y , can you tell me where I made a mistake.

Thanks in advance

Regor60 · Answer

Faulty question IMO.

If B=0 then A=0 and X and Y could be anything, although "anything" isn't among the answer choices.

Similarly, if A=B=X=Y=1, then

X=Y, which is among the answer choices and the given answer would be incorrect since it doesn't yield Y=1 when X=1 is substituted.

For this question to make sense limitations would have to be placed on the domain

If a^x = b^y = ab, then find the value of y

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