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

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Director
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If a^x = b^y = ab, then find the value of y  [#permalink]

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New post Updated on: 22 Apr 2019, 00:39
4
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

47% (02:03) correct 53% (02:07) wrong based on 36 sessions

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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

Originally posted by nick1816 on 21 Apr 2019, 23:13.
Last edited by Bunuel on 22 Apr 2019, 00:39, edited 1 time in total.
Renamed the topic and edited the question.
Manager
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Re: If a^x = b^y = ab, then find the value of y  [#permalink]

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New post 22 Apr 2019, 04:18
2
\(a^{x} = ab\)
\(a^{(x-1)} = b\) -- (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
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Re: If a^x = b^y = ab, then find the value of y   [#permalink] 22 Apr 2019, 04:18
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If a^x = b^y = ab, then find the value of y

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