BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

stuck on exponents

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 36
Joined: Sat Apr 14, 2007 8:06 am

stuck on exponents

by allenkt » Tue May 08, 2007 10:12 am
I hate exponents....

5^21 x 4^11 = 2 x 10^n solve for n

a) 11
b) 21
c) 22
d) 23
e) 32

I'm lost here. Since the bases are different ( 5 and 4) I don't know what I can do to simplify this. I suppose I could try to find the 21st power of 5 and the 11th power of 4 and do it the hard way but I'd be here for half the test doing that.
Top
Source: — Problem Solving |
Legendary Member
Posts: 559
Joined: Tue Mar 27, 2007 1:29 am
Thanked: 5 times
Followed by:2 members

by Cybermusings » Tue May 08, 2007 11:11 am
5^21 x 4^11 = 2 x 10^n

5^21 * 2^22 = 2 * 2^n * 5^n
5^21 * 2^22 = 2^n+1 * 5^n
Since bases are same you can equate the exponents
Hence n = 21
Top
Senior | Next Rank: 100 Posts
Posts: 36
Joined: Sat Apr 14, 2007 8:06 am

by allenkt » Tue May 08, 2007 1:34 pm
How did you go from 5^21 * 4^11

to

5^21 * 2^22?

Putting in my calculator I can see that 4^11 = 2^22 but I'm not sure why as it doesn't work with all numbers. For instance....ahhh...never mind. I was trying to divide the first number by 2, then multiply the exponent by 2 but that obviously wasn't working. Then I realized 2 was the square root of 4 and tried some other numbers. For instance, 9^11 = 3^22.

So you can take the square root of the base and double the exponent and the value is the same? I didn't know you could do that. I also would never have thought of taking 2 * 2^n and making it 2^n+1.

Thanks for the explanation!
Top
Senior | Next Rank: 100 Posts
Posts: 36
Joined: Sat Apr 14, 2007 8:06 am

by allenkt » Tue May 08, 2007 1:49 pm
Even after the explanation this one was hard so I want to write it out for anyone else struggling with it:

5^21 * 4^11 = 2 * 10^n

5^21 * 2^22 = 2 * 2^n * 5^n

5^21 * 2^22 = 2^n+1 * 5^n

2^n+1 / 2^22 * 5^n / 5^21 = 1

2^n+1-22 * 5^n-21 = 1

2^n-21 * 5^n-21 = 1

10^n-21 = 1

Now, since we know that anything raised to the zero power is 1 we can say

10^0 = 1 therefore

10^n-21 = 10^0 = 1 therefore

n-21 = 0

n = 21
Top
Junior | Next Rank: 30 Posts
Posts: 27
Joined: Thu May 03, 2007 2:20 am
Location: India

by abkhan » Mon May 21, 2007 5:11 am
sorry but cybermusing seems easier. try breaking any given number into prime numbers. they tend to show a much more clearer relation

5^21 * 4^11 = 2 * 10^n
=> 5^21 * (2^2)^11 = 2 * 10^n
=> 5^21 * 2^22 = 2 * 10^n
=> 2 * 10^21 = 2 * 10^n
equating n on both sides
we have n=21
I am ..therefore I am..
Top
Post new topic Post Reply
• Page 1 of 1