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

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M7MBA: Moderator; Posts: 2058; Joined: Sun Oct 29, 2017 4:24 am; Thanked: 1 times; Followed by:5 members

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

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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Source: Beat The GMAT — Problem Solving | Sat Apr 28, 2018 1:31 am

Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pm; Thanked: 6 times; Followed by:5 members

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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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

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 1/5Â²)
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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