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If 5^x = y, what is x?

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If 5^x = y, what is x? [#permalink]

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

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New post 04 Nov 2014, 20:08
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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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New post 04 Nov 2014, 20:38
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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Re: If 5^x = y, what is x? [#permalink]

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New post 04 Nov 2014, 22:05
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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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Re: If 5^x = y, what is x? [#permalink]

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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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New post 04 Nov 2014, 23:39
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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Re: If 5^x = y, what is x? [#permalink]

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New post 05 Nov 2014, 02:15
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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?

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

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New post 09 Feb 2018, 00:45
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Re: If 5^x = y, what is x?   [#permalink] 09 Feb 2018, 00:45
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