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# If (25[square_root]5[/square_root])^x=(\sqrt[3]{5})^{x+1}

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Math Expert
Joined: 02 Sep 2009
Posts: 59588

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13 Mar 2015, 07:55
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Difficulty:

25% (medium)

Question Stats:

78% (01:58) correct 22% (02:33) wrong based on 109 sessions

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If $$(25\sqrt{5})^x=(\sqrt[3]{5})^{x+1}$$, what does x equal

(A) 1/5
(B) 2/13
(C) 2/15
(D) 5/3
(E) 15/2

Kudos for a correct solution.

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Joined: 07 Aug 2011
Posts: 499
GMAT 1: 630 Q49 V27

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13 Mar 2015, 08:11
1
Bunuel wrote:
If $$(25\sqrt{5})^x=(\sqrt[3]{5})^{x+1}$$, what does x equal

(A) 1/5
(B) 2/13
(C) 2/15
(D) 5/3
(E) 15/2

Kudos for a correct solution.

$$(5/2)X=1/3 (X+1)$$
$$X=2/13$$
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Joined: 28 Feb 2014
Posts: 289
Location: United States
Concentration: Strategy, General Management

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13 Mar 2015, 08:20
Bunuel wrote:
If $$(25\sqrt{5})^x=(\sqrt[3]{5})^{x+1}$$, what does x equal

(A) 1/5
(B) 2/13
(C) 2/15
(D) 5/3
(E) 15/2

Kudos for a correct solution.

25^x × 5^x/2 = (5^1/3)^(x+1)
(25^x × 5^x/2)/(5^x/3 +1/3) = 1
5^(x/6 - 1/3) = 5^-2x
13x/6 = 1/3
x = 2/13

Director
Joined: 21 May 2013
Posts: 633

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15 Mar 2015, 05:34
1
Bunuel wrote:
If $$(25\sqrt{5})^x=(\sqrt[3]{5})^{x+1}$$, what does x equal

(A) 1/5
(B) 2/13
(C) 2/15
(D) 5/3
(E) 15/2

Kudos for a correct solution.

+1 for B. (5^2*5^1/2)^X=5^X+1/3
5/2X=X+1/3
15X=2X+2
X=2/13
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Joined: 18 Aug 2014
Posts: 111
Location: Hong Kong
Schools: Mannheim

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15 Mar 2015, 06:24
KS15 wrote:
Bunuel wrote:
If $$(25\sqrt{5})^x=(\sqrt[3]{5})^{x+1}$$, what does x equal

(A) 1/5
(B) 2/13
(C) 2/15
(D) 5/3
(E) 15/2

Kudos for a correct solution.

+1 for B. (5^2*5^1/2)^X=5^X+1/3
5/2X=X+1/3
15X=2X+2
X=2/13

Hi, how do you get from first step to the second one? (5/2x = x + 1/3)
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Joined: 13 Mar 2015
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15 Mar 2015, 20:50
2
(25^x)($$\sqrt{5}$$^x)= $$\sqrt[3]{5}$$^x+1
(5^2x)(5^x/2)= (5^(x+1/3))
(5^(4x/2))(5^x/2)= (5^(x+1/3))
(5^(5x/2))= (5^(x+1/3))

5x/2=x+1/3 cross multiply
15x=2x+2
13x=2
x=2/13
Math Expert
Joined: 02 Sep 2009
Posts: 59588

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15 Mar 2015, 23:00
1
2
Bunuel wrote:
If $$(25\sqrt{5})^x=(\sqrt[3]{5})^{x+1}$$, what does x equal

(A) 1/5
(B) 2/13
(C) 2/15
(D) 5/3
(E) 15/2

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:

We need to express each side as a power of 5. We will use fractional exponents for the roots.
Attachment:

cgpwe_img34.png [ 3.83 KiB | Viewed 2041 times ]

Equate the exponents.
Attachment:

cgpwe_img35.png [ 937 Bytes | Viewed 2041 times ]

Multiply both sides by 6 to clear the fractions.
Attachment:

cgpwe_img36.png [ 2.07 KiB | Viewed 2041 times ]

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17 Mar 2015, 03:07
Making bases of both the sides 5, so that the powers can be equated

$$(5^2 * 5^{\frac{1}{2}})^x = 5^{\frac{1}{3} * (x+1)}$$

Equating the powers

$$\frac{5}{2} * x = \frac{1}{3} *(x+1)$$

$$x = \frac{2}{13}$$

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Joined: 09 Sep 2013
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24 Mar 2019, 07:43
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Re: If (25[square_root]5[/square_root])^x=(\sqrt[3]{5})^{x+1}   [#permalink] 24 Mar 2019, 07:43
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