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

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VP
Joined: 19 Oct 2018
Posts: 1151
Location: India
If a^x = b^y = ab, then find the value of y  [#permalink]

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Updated on: 22 Apr 2019, 00:39
4
00:00

Difficulty:

55% (hard)

Question Stats:

49% (02:02) correct 51% (02:09) wrong based on 39 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
Joined: 05 Oct 2017
Posts: 79
Re: If a^x = b^y = ab, then find the value of y  [#permalink]

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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
Re: If a^x = b^y = ab, then find the value of y   [#permalink] 22 Apr 2019, 04:18
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