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Exponents, power manipulation

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by Brent@GMATPrepNow » Mon Jan 28, 2013 10:26 am
kittenko wrote:Hello,
I can't get to the right answer in this one
(5^21)(4^11)= 2(10^x)

value of x?

1. 23
2. 21
3. 11
4. 138
5. 56
One approach:

(5^21)(4^11)= 2[10^x]
(5^21)((2^2)^11) = 2(2^x)(5^x)
(5^21)(2^22) = 2(2^x)(5^x)
(5^21)(2^1)(2^21) = 2(2^x)(5^x)
Divide both sides by 2 to get:
(5^21)(2^21) = (2^x)(5^x)
x = 21

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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GMAT/MBA Expert

User avatar
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 » Mon Jan 28, 2013 10:30 am
kittenko wrote: (5^21)(4^11)= 2(10^x)
Value of x?

1. 23
2. 21
3. 11
4. 138
5. 56
Or we can just see that

(5^21)(4^11)= 2[10^x]
(5^21)(4^11) = 2(2^x)(5^x)
At this point, we can see that the powers of 5 must be equal.
So, x = 21

Note: In the first step, I applied a nice law that says (xy)^n = (x^n)(y^n)

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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