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If 25(5^x) = 1 then x=

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If 25(5^x) = 1 then x= [#permalink]

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If 25(5^x) = 1 then x=

A. –2
B. –1
C. 0
D. 1
E. 2

[Reveal] Spoiler:
I have probelm with this question .
I solved it like 5^2(5^x)=1
2+x=1
X=-1

But my answer is wrong or the answer from the source is wrong please help ....
[Reveal] Spoiler: OA
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Re: If 25(5^x) = 1 then x= [#permalink]

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New post 25 Nov 2010, 00:53
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rite2deepti wrote:
If 25(5^x)=1 then x=
A. –2
B. –1
C. 0
D. 1
E. 2

I have probelm with this question .
I solved it like 5^2(5^x)=1
2+x=1
X=-1

But my answer is wrong or the answer from the source is wrong please help ....



\(25*5^x=1\) --> \(5^2*5^x=1\) --> \(5^{2+x}=1\) --> \(2+x=0\) (\(a^0=1\) - any nonzero number to the power of 0 is 1) --> \(x=-2\).

Answer: A.
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Re: If 25(5^x) = 1 then x= [#permalink]

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New post 31 Dec 2017, 00:16
rite2deepti wrote:
If 25(5^x) = 1 then x=

A. –2
B. –1
C. 0
D. 1
E. 2

[Reveal] Spoiler:
I have probelm with this question .
I solved it like 5^2(5^x)=1
2+x=1
X=-1

But my answer is wrong or the answer from the source is wrong please help ....


\(5^2\)\(5^x\)=1

\(5^x\) = 1/\(5^2\)

\(5^x\) = \(5^-2\)

If bases are same then we can equate powers

Therefore x = -2
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Re: If 25(5^x) = 1 then x= [#permalink]

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New post 31 Dec 2017, 08:15
rite2deepti wrote:
If 25(5^x) = 1 then x=

A. –2
B. –1
C. 0
D. 1
E. 2

[Reveal] Spoiler:
I have probelm with this question .
I solved it like 5^2(5^x)=1
2+x=1
X=-1

But my answer is wrong or the answer from the source is wrong please help ....



Hey Deepti,

You have solved the question correctly till this point:

\(5^{(2+x)} = 1\)

But please remember that while equating the powers from LHS and RHS, the base should be the same. In the LHS, the base is 5 and on the right hand side(RHS), the base is 1, so we need to convert 1 to the base 5, which can be easily done, by write 1 as \(5^0\)

Now you will have \(5^{(2+x)} = 5^0\)

After this, you can equate the powers, which will give you \(2 + x = 0\) and \(x = -2\)

I hope this clears your doubt.


Regards,
Saquib
e-GMAT
Quant Expert
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Re: If 25(5^x) = 1 then x=   [#permalink] 31 Dec 2017, 08:15
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