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# If y^(3x) = 5^x and y is a positive number, what is x?

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Math Expert
Joined: 02 Sep 2009
Posts: 41891

Kudos [?]: 128912 [0], given: 12183

If y^(3x) = 5^x and y is a positive number, what is x? [#permalink]

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24 Sep 2017, 23:56
Expert's post
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Difficulty:

55% (hard)

Question Stats:

50% (00:42) correct 50% (01:18) wrong based on 26 sessions

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If $$y^{(3x)} = 5^x$$ and y is a positive number, what is x?

(1) $$y = \sqrt[3]{5}$$

(2) $$y^x=5^{(\frac{x}{3})}$$
[Reveal] Spoiler: OA

_________________

Kudos [?]: 128912 [0], given: 12183

Senior Manager
Joined: 02 Jul 2017
Posts: 252

Kudos [?]: 59 [0], given: 59

Location: India
Re: If y^(3x) = 5^x and y is a positive number, what is x? [#permalink]

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25 Sep 2017, 03:03
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If $$y^{3x}=5^x$$ and y is a positive number, what is x?

$$y^{3x}=5^x$$
=> $$(y^3)^x=5^x$$
=> $$y^3=5$$
=> $$y=5^\frac{1}{3}$$

(1) $$y= \sqrt[3]5$$
=> $$y^3 = 5$$
This is already given in question stem. As no detail about x given.
Insufficient

(2) $$y^x=5^\frac{x}{3}$$
=> $$y^x=(5^\frac{1}{3})^x$$
=> $$y=5^\frac{1}{3}$$
This is already given in question stem. As no detail about x given.
Insufficient

1+2
Here also we don't get any information about x

Kudos [?]: 59 [0], given: 59

Re: If y^(3x) = 5^x and y is a positive number, what is x?   [#permalink] 25 Sep 2017, 03:03
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