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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: 56369
If y^(3x) = 5^x and y is a positive number, what is x?  [#permalink]

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24 Sep 2017, 23:56
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Difficulty:

55% (hard)

Question Stats:

58% (01:29) correct 42% (01:40) wrong based on 121 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) $$y^x=5^{(\frac{x}{3})}$$

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Joined: 02 Jul 2017
Posts: 292
Concentration: Entrepreneurship, Technology
GMAT 1: 730 Q50 V38
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
1
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

Manager
Joined: 19 Jun 2017
Posts: 55
Location: India
GPA: 3.23
Re: If y^(3x) = 5^x and y is a positive number, what is x?  [#permalink]

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26 Feb 2018, 10:00
Nikkb wrote:
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

Why can't we use the information given in the statement 1 and substitute it in the stem "y"??
Retired Moderator
Joined: 25 Feb 2013
Posts: 1196
Location: India
GPA: 3.82
Re: If y^(3x) = 5^x and y is a positive number, what is x?  [#permalink]

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26 Feb 2018, 10:45
sahilsnpt wrote:
Nikkb wrote:
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

Why can't we use the information given in the statement 1 and substitute it in the stem "y"??

Hi sahilsnpt

our objective is to find the value of x and as explained in the above solution both statement 1 & the question stem gives the same information. So it will not lead to any solution. Just for practice, try substituting the value of y from statement 1 in the question stem and see if you are getting any value for x
Manager
Joined: 19 Jun 2017
Posts: 55
Location: India
GPA: 3.23
Re: If y^(3x) = 5^x and y is a positive number, what is x?  [#permalink]

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27 Feb 2018, 12:15
niks18 wrote:
sahilsnpt wrote:
Nikkb wrote:
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

Why can't we use the information given in the statement 1 and substitute it in the stem "y"??

Hi sahilsnpt

our objective is to find the value of x and as explained in the above solution both statement 1 & the question stem gives the same information. So it will not lead to any solution. Just for practice, try substituting the value of y from statement 1 in the question stem and see if you are getting any value for x

No,I am not getting any solution of X.Thank you for the explanation!
Re: If y^(3x) = 5^x and y is a positive number, what is x?   [#permalink] 27 Feb 2018, 12:15
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