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

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

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New post 13 Mar 2015, 07:55
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79% (01:55) correct 21% (02:43) wrong based on 95 sessions

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

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New post 13 Mar 2015, 08:11
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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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Re: If (25[square_root]5[/square_root])^x=(\sqrt[3]{5})^{x+1}  [#permalink]

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New post 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

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

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

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

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New post 15 Mar 2015, 20:50
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(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
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Re: If (25[square_root]5[/square_root])^x=(\sqrt[3]{5})^{x+1}  [#permalink]

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New post 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
cgpwe_img34.png [ 3.83 KiB | Viewed 1871 times ]

Equate the exponents.
Attachment:
cgpwe_img35.png
cgpwe_img35.png [ 937 Bytes | Viewed 1871 times ]

Multiply both sides by 6 to clear the fractions.
Attachment:
cgpwe_img36.png
cgpwe_img36.png [ 2.07 KiB | Viewed 1871 times ]


Answer = (B).
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Re: If (25[square_root]5[/square_root])^x=(\sqrt[3]{5})^{x+1}  [#permalink]

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New post 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

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

\(x = \frac{2}{13}\)

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

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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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