exponents problem

by **Guest** Mon Oct 27, 2008 1:45 pm

can someone help me think through how to do this problem-

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

what is n

by **Guest** Mon Oct 27, 2008 2:08 pm

do people only respond if it is a MGMAT question?

by **Saurav** Wed Oct 29, 2008 3:02 pm

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

what is n

simplify left side of equality

5^21 * 4^11
= 5 ^21 * (2^2)^11
= 5 ^21 * 2^22

simplify right side of equality
2 * 10^n
= 2 * (5 * 2)^n
= 2 * 5^n * 2^n
= 5 ^n * 2^(n+1)

hence
5 ^21 * 2^22 = 5 ^n * 2^(n+1)

compare exponents on both sides to get value of n=21

by **Saurav** Wed Oct 29, 2008 3:04 pm

if you reply to your post within minutes of putting in the forum, it will show 1 reply, which is most likely considered as the question being replied. hence many people might skip looking inside. I just happen to read inside to see the question myself and saw this was not answered.

Anonymous Wrote:do people only respond if it is a MGMAT question?

by **esledge** Sun Nov 16, 2008 5:15 pm

Thanks for responding, Saurav. Well done.

Take-aways: Try to match bases on each side of the equal sign, so that you will be allowed to match exponents. Typically, breaking all bases down to their prime factors is the way to go, though not necessary every time (e.g. if you have 10^k = 10^17, then there is no need to break 10 down further to 2 and 5.)