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If 2^y = 4^(5x + 3) and 3^(x - 7) = 9^y, what is the value of x + y ?

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If 2^y = 4^(5x + 3) and 3^(x - 7) = 9^y, what is the value of x + y ?  [#permalink]

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New post Updated on: 30 Nov 2014, 05:58
2
4
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

79% (02:16) correct 21% (02:48) wrong based on 187 sessions

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If 2^y = 4^(5x + 3) and 3^(x - 7) = 9^y, what is the value of x + y ?

A. -10
B. -5
C. -4
D. 3
E. 7

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Originally posted by FTS185 on 29 Nov 2014, 19:10.
Last edited by Bunuel on 30 Nov 2014, 05:58, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
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Re: If 2^y = 4^(5x + 3) and 3^(x - 7) = 9^y, what is the value of x + y ?  [#permalink]

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New post 30 Nov 2014, 05:58
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Re: If 2^y = 4^(5x + 3) and 3^(x - 7) = 9^y, what is the value of x + y ?  [#permalink]

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New post 30 Nov 2014, 06:22
1
2^y = 4^(5x + 3)
2^y=2^2(5x+3)
y=10x+6 ........... 1

3^(x - 7) = 9^y
3^(x-7)=3^2y
x-7=2y ............. 2

put value of y=10x+6 in eq 2
x-7=2(10x+6)
x-7=20x+12
19x=-19
x=-1

therefore, y= -10+6
y=-4

x+y= -1-4= -5

Ans - B
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Re: If 2^y = 4^(5x + 3) and 3^(x - 7) = 9^y, what is the value of x + y ?  [#permalink]

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New post 01 Dec 2014, 00:45
2
\(2^y = 4^{(5x + 3)}\)

\(2^y = 2^{2(5x+3)}\)

y = 10x+6 ........... (1)

\(3^{(x - 7)} = 9^y\)

\(3^{(x-7)}=3^{2y}\)

x-7 = 2y ............. (2)

x-7 = 2*(10x+6)

x = -1 & y = -4

x+y = -1 -4 = -5

Answer = B
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Re: If 2^y = 4^(5x + 3) and 3^(x - 7) = 9^y, what is the value of x + y ?  [#permalink]

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New post 22 Oct 2018, 00:33
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Re: If 2^y = 4^(5x + 3) and 3^(x - 7) = 9^y, what is the value of x + y ?   [#permalink] 22 Oct 2018, 00:33
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