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# If 5^x = y, what is x?

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Math Expert
Joined: 02 Sep 2009
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If 5^x = y, what is x? [#permalink]

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04 Nov 2014, 10:03
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Tough and Tricky questions: Exponents.

If 5^x = y, what is x?

(1) y^2 = 625
(2) y^3 = 15,625

Kudos for a correct solution.

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Manager
Joined: 22 Sep 2012
Posts: 140
Concentration: Strategy, Technology
WE: Information Technology (Computer Software)
Re: If 5^x = y, what is x? [#permalink]

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04 Nov 2014, 21:08
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5^x = y

We can therefore say, x = y^(1/5)

Statement 1. y^2 = 625
y can be +25 or -25

Since x,y should be real number y cannot be -ve. Therefore,
x= 25^(1/5). Sufficient

Statement 2.
y^3=15625
therefore y = 25 and x = 25^(1/5). Sufficient.

Hence the answer is D)
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Re: If 5^x = y, what is x? [#permalink]

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04 Nov 2014, 21:38
kinghyts wrote:
5^x = y

We can therefore say, x = y^(1/5)

Statement 1. y^2 = 625
y can be +25 or -25

Since x,y should be real number y cannot be -ve. Therefore,
x= 25^(1/5). Sufficient

Statement 2.
y^3=15625
therefore y = 25 and x = 25^(1/5). Sufficient.

Hence the answer is D)

St1 says y^2=625.. Since LHS and RHS are greater than zero..We can take square root on both sides and get
$$\sqrt{y^2}=\sqrt{625}$$

or |y|=25 or y=+/-25 So x can have 2 values...

A is not sufficient..

If y=-25 then x=-2 and if y=25 then x=2

Ans is B as y^3=15625=positive...so y will have the same sign an y^3 so y is positive
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Location: United States
Re: If 5^x = y, what is x? [#permalink]

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04 Nov 2014, 23:05
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Theories: if $$a >= 0$$ then$$a^x > 0$$

(*) So $$5^x > 0$$, AND $$5^x = y$$
--> y must be positive.

S1: $$y^2 = 625$$ --> $$y = 25$$ OR $$y = -25$$
From (*), y must be positive --> y is only 25
-->$$5^x = 25 = 5^2$$
--> $$x = 2$$
S1 is sufficient

S2: $$y^3 = 15,625 = 25^3 --> y = 25$$
--> $$5^x = 25 = 5^2$$
--> $$x = 2$$
S2 is sufficient

Ans: D
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Joined: 31 Jul 2014
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GMAT 1: 630 Q48 V29
Re: If 5^x = y, what is x? [#permalink]

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05 Nov 2014, 00:08
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WoundedTiger wrote:
kinghyts wrote:
5^x = y

We can therefore say, x = y^(1/5)

Statement 1. y^2 = 625
y can be +25 or -25

Since x,y should be real number y cannot be -ve. Therefore,
x= 25^(1/5). Sufficient

Statement 2.
y^3=15625
therefore y = 25 and x = 25^(1/5). Sufficient.

Hence the answer is D)

St1 says y^2=625.. Since LHS and RHS are greater than zero..We can take square root on both sides and get
$$\sqrt{y^2}=\sqrt{625}$$

or |y|=25 or y=+/-25 So x can have 2 values...

A is not sufficient..

If y=-25 then x=-2 and if y=25 then x=2

Ans is B as y^3=15625=positive...so y will have the same sign an y^3 so y is positive

5^x = y , so if you take x=-2 , it willbe 1/25 rt and we cant equate it with 25....
so y=-25 then x=-2 -> how is it correct?
Also, in 5^x = y we know LHS has positive base so RHS also should have positive base
so 5^x can be equated only to 25, rt?
Please clarify me.
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Re: If 5^x = y, what is x? [#permalink]

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05 Nov 2014, 00:39
anupamadw wrote:
WoundedTiger wrote:
kinghyts wrote:
5^x = y

We can therefore say, x = y^(1/5)

Statement 1. y^2 = 625
y can be +25 or -25

Since x,y should be real number y cannot be -ve. Therefore,
x= 25^(1/5). Sufficient

Statement 2.
y^3=15625
therefore y = 25 and x = 25^(1/5). Sufficient.

Hence the answer is D)

St1 says y^2=625.. Since LHS and RHS are greater than zero..We can take square root on both sides and get
$$\sqrt{y^2}=\sqrt{625}$$

or |y|=25 or y=+/-25 So x can have 2 values...

A is not sufficient..

If y=-25 then x=-2 and if y=25 then x=2

Ans is B as y^3=15625=positive...so y will have the same sign an y^3 so y is positive

5^x = y , so if you take x=-2 , it willbe 1/25 rt and we cant equate it with 25....
so y=-25 then x=-2 -> how is it correct?
Also, in 5^x = y we know LHS has positive base so RHS also should have positive base
so 5^x can be equated only to 25, rt?
Please clarify me.

Well...I goofed up on this one to be honest...Multitasking does this to you...
Ans has to be D..

Thanks for pointing out
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Joined: 10 Apr 2008
Posts: 25
Location: India
GMAT 1: 560 Q39 V28
WE: Consulting (Computer Software)
Re: If 5^x = y, what is x? [#permalink]

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05 Nov 2014, 03:15
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I guess ans has to be D.

A - we get two options for y when y ^ 2 = 625 > +25 & -25. However, if we take a look at original statement 5 ^ x = y, only raising 5 to power of 4 will give 625. -ve sign is maintained only for odd powers and therefore, even though -25 is one of the values, it is not valid. Hence A is suff.

B - y ^ 3 = 15625 > this says that y is +ve and we can obtain unique value for X from this option. Hence B is suff.

Ans D. My I missing anything here?

Ameya
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Posts: 6826
Re: If 5^x = y, what is x? [#permalink]

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09 Feb 2018, 01:45
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Re: If 5^x = y, what is x?   [#permalink] 09 Feb 2018, 01:45
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# If 5^x = y, what is x?

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