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

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Intern
Joined: 02 Sep 2010
Posts: 42
If 25(5^x) = 1 then x=  [#permalink]

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25 Nov 2010, 01:49
1
00:00

Difficulty:

5% (low)

Question Stats:

78% (00:31) correct 22% (00:40) wrong based on 112 sessions

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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

Math Expert
Joined: 02 Sep 2009
Posts: 50000
Re: If 25(5^x) = 1 then x=  [#permalink]

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25 Nov 2010, 01:53
1
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

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

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

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31 Dec 2017, 01:16
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

$$5^2$$$$5^x$$=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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Joined: 04 Jan 2015
Posts: 2066
Re: If 25(5^x) = 1 then x=  [#permalink]

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31 Dec 2017, 09:15
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

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

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04 May 2018, 10:31
rite2deepti wrote:
If 25(5^x) = 1 then x=

A. –2
B. –1
C. 0
D. 1
E. 2

(5^2)(5^x) = 5^0

5^(2 + x) = 5^0

2 + x = 0

x = -2

Alternate Solution:

25(5^x) = 1

5^x = 1/25

5^x = 5^-2

x = -2

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Re: If 25(5^x) = 1 then x= &nbs [#permalink] 04 May 2018, 10:31
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