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# If 5^(x + y) = 125 and 3^(x − 3y) = 1/9, then y =

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Joined: 02 Sep 2009
Posts: 58427
If 5^(x + y) = 125 and 3^(x − 3y) = 1/9, then y =  [#permalink]

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24 Aug 2018, 01:20
00:00

Difficulty:

15% (low)

Question Stats:

81% (01:36) correct 19% (01:50) wrong based on 45 sessions

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If $$5^{(x+y)} = 125$$ and $$3^{(x−3y)} = \frac{1}{9}$$, then y =

A. −5/2
B. 1/4
C. 1/2
D. 5/2
E. 5/4

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If 5^(x + y) = 125 and 3^(x − 3y) = 1/9, then y =  [#permalink]

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24 Aug 2018, 01:25
$$5^{(x+y)}$$ = 125

or $$5^{(x+y)}$$ = $$5^3$$

x+y = 3......(1)

Also,

$$3^{(x−3y)}$$ = $$\frac{1}{9}$$ = $$\frac{1}{3^2}$$ or $$3^{-2}$$

x-3y = -2.......(2)

Solving 1 and 2 gives 5 = 4y or Y = $$\frac{5}{4}$$.
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Re: If 5^(x + y) = 125 and 3^(x − 3y) = 1/9, then y =  [#permalink]

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24 Aug 2018, 01:30
Bunuel wrote:
If $$5^{(x+y)} = 125$$ and $$3^{(x−3y)} = \frac{1}{9}$$, then y =

A. −5/2
B. 1/4
C. 1/2
D. 5/2
E. 5/4

$$5^{(x+y)} = 125$$
Or, $$5^{(x+y)} = 5^3$$
Or, x+y=3-----(1)

$$3^{(x−3y)} = \frac{1}{9}$$=$$3^{-2}$$
Or, x-3y=-2--(2)
From(1) and (2), we have,

4y=5
Or, y=5/4

Ans. (E)
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Re: If 5^(x + y) = 125 and 3^(x − 3y) = 1/9, then y =  [#permalink]

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24 Aug 2018, 01:54
Bunuel wrote:
If $$5^{(x+y)} = 125$$ and $$3^{(x−3y)} = \frac{1}{9}$$, then y =

A. −5/2
B. 1/4
C. 1/2
D. 5/2
E. 5/4

Given ,

$$5^{(x + y)} = 5^3$$

x + y = 3

and

$$3^{(x - 3y)}= 3^{(-2)}$$

x - 3y = -2

We are asked to find out the value of y.

x + y - (x - 3y) = 3 - (-2)

x + y - x + 3y = 5

4y = 5

y =$$\frac{5}{4}$$

Re: If 5^(x + y) = 125 and 3^(x − 3y) = 1/9, then y =   [#permalink] 24 Aug 2018, 01:54
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