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

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by M7MBA » Sat Apr 28, 2018 1:31 am
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If 25(5^x) = 1 then x=

A. –2
B. –1
C. 0
D. 1
E. 2

The OA is A.

To solve this PS question should I plug in the values? I'd appreciate some help here. Thanks.
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by Vincen » Sat Apr 28, 2018 2:31 am
Hi gmat_mission.

You can plug in the values or you can solve it algebraically as follows: $$25\left(5^x\right)=1\ \ \Rightarrow\ \ 5^2\cdot5^x=1$$ $$\Rightarrow \ 5^{2+x}=5^0$$ $$\Rightarrow\ \ 2+x=0$$ $$\Rightarrow\ \ x=-2.$$ Hence, the correct answer is the option [spoiler]A=-2[/spoiler].

I hope it helps you.
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by Brent@GMATPrepNow » Wed May 02, 2018 1:02 pm
M7MBA wrote:If 25(5^x) = 1 then x=

A. –2
B. –1
C. 0
D. 1
E. 2
Given: (25)(5^x) = 1
Divide both sides by 25 to get: 5^x = 1/25 (aka 1/5²)
Rewrite 1/25 as 5^(-2) to get: 5^x = 5^(-2)
So, x = -2

Answer: A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Jeff@TargetTestPrep » Fri May 04, 2018 9:33 am
M7MBA 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

Answer: A

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