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555-605 (Medium)|   Algebra|   Exponents|      
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FTS185
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If 2^y = 4^(5x + 3) and 3^(x - 7) = 9^y, what is the value of x + y ? Updated on: 30 Nov 2014, 05:58
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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B
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25% (medium)

Question Stats:

82% (02:12) correct 18% (02:36) wrong based on 497 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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B

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If 2^y = 4^(5x + 3) and 3^(x - 7) = 9^y, what is the value of x + y ? 30 Nov 2014, 05:58
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FTS185
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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\(2^y = 4^{(5x + 3)}\) --> \(2^y = 2^{2(5x + 3)}\) --> \(y = 2(5x + 3)\);

\(3^{(x - 7)} = 9^y\) --> \(3^{(x - 7)} = 3^{2y}\) --> \(x-7=2y\).

From above \(x = -1\) and \(y=-4\) --> \(x +y = -5\).

Answer: B.
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If 2^y = 4^(5x + 3) and 3^(x - 7) = 9^y, what is the value of x + y ? 30 Nov 2014, 06:22
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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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If 2^y = 4^(5x + 3) and 3^(x - 7) = 9^y, what is the value of x + y ? 01 Dec 2014, 00:45
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\(2^y = 4^{(5x + 3)}\)

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

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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If 2^y = 4^(5x + 3) and 3^(x - 7) = 9^y, what is the value of x + y ? 22 Jun 2026, 05:57
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Day 1 of 45: Daily Question 1 (written from mobile)
- Exploring Exponents and Equations
* Like Bases (exponents)
* Equal sign represents the same value on both sides
2^y = 4^(5x+3)
2^y = 2^2^^(5x+3)
^^ multiply (5x+3) by 2
y = 10x + 6

3^(x-7) = 9^y
3^(x-7) = 3^2^^(10x+6)
^^ multiply (10x+6) by 2
x-7 = 20x +12
x = -1

x+y = 10(-1)+6-1
x+y = -5
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If 2^y = 4^(5x + 3) and 3^(x - 7) = 9^y, what is the value of x + y ? 22 Jun 2026, 07:51
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FTS185
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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2^y=4^(5x+3)
2^y=2^2(5x+3)
y=2(5x+3)
y=10x+6---(1)

3^(x - 7) = 9^y
3^(x-7)=3^2y
x-7=2y---(2)
putting eq(1)in eq(2)
x-7=20x+12
-19=19x
x=-1
y=-10+6=-4
x+y=-5
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