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If 75^y*27^(2y + 1) = 5^4*3^x, what is the value of x?

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If 75^y*27^(2y + 1) = 5^4*3^x, what is the value of x? [#permalink]

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New post 25 Apr 2017, 02:39
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E

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  25% (medium)

Question Stats:

77% (01:30) correct 23% (02:21) wrong based on 163 sessions

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Re: If 75^y*27^(2y + 1) = 5^4*3^x, what is the value of x? [#permalink]

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New post 25 Apr 2017, 02:47
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write it as (25*3)^y * (3^3)^2y+1
= (5^2)^y * 3^y * 3^6y+3
= 5^2y * 3^7y+3
now it is given that this is equal to 5^4 * 3^x

so Equating the powers of these prime numbers we get
2y=4, means y = 2
x= 7y+3 = 14+3 = 17
Hence E

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If 75^y*27^(2y + 1) = 5^4*3^x, what is the value of x? [#permalink]

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New post Updated on: 30 Apr 2017, 08:27
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If 75^y*27^(2y + 1) = 5^4*3^x, what is the value of x?

(A) 8
(B) 10
(C) 12
(D) 15
(E) 17

\(75^y\)*27^(2y+1)=(5^2)^y * 3^y *(3^3)^(2y+1) = (5^2)^y *3^ (7y+3)
2y= 4, y=2
x= 7y+3= 17
So correct answer is E) 17

Originally posted by sreenu7464 on 30 Apr 2017, 06:43.
Last edited by sreenu7464 on 30 Apr 2017, 08:27, edited 2 times in total.
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If 75^y*27^(2y + 1) = 5^4*3^x, what is the value of x? [#permalink]

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New post 30 Apr 2017, 08:19
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Bunuel wrote:
If \(75^y*27^{(2y + 1)} = 5^4*3^x\), what is the value of x?

(A) 8
(B) 10
(C) 12
(D) 15
(E) 17


\(75^y \times 27^{(2y + 1)} = 5^4\times 3^x \\
\implies (3\times 5^2)^y \times (3^3)^{2y+1}=5^4\times 3^x \\
\implies 3^y\times 5^{2y}\times 3^{3(2y+1)}=5^4\times 3^x \\
\implies 5^{2y}\times 3^{y+3(2y+1)}=5^4\times 3^x \)
\(\implies 2y=4\) and \(y+3(2y+1)=x\)
\(\implies y=2\) and \(x=2+3(2\times 2+1)=17\)

The answer is E
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Re: If 75^y*27^(2y + 1) = 5^4*3^x, what is the value of x? [#permalink]

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New post 08 Jun 2018, 10:50
(3*5*5)^y *((3)^3)^2y+1 = 5^4*3^x
5^2y=5^4 ,therefore y=2
and 3^y*3^6y*3^3 and therefore putting y=2 ,x =17
Re: If 75^y*27^(2y + 1) = 5^4*3^x, what is the value of x?   [#permalink] 08 Jun 2018, 10:50
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