Hi sauberheine1,
This question is all about how you "rewrite" exponents. Before I go through the explanation, I have to ask if this question was transcribed correctly - are we supposed to solve for the value of M or the value of S?
Here, we're given (2^15)(25^S) = 5(10^M). Here's how we can solve for the value of M.
On the "left side":
(2^15) we'll leave alone
(25^S) can be rewritten as (5^2)^S = 5^(2S)
On the "right side":
5 can be written as 5^1
(10^M) can be rewritten as [(2)(5)]^M = (2^M)(5^M)
So now the overall equation is...
(2^15)[5^(2S)] = (5^1)(5^M)(2^M)
Looking at the "base 2" part of each side, we have...(2^15) and (2^M), so M MUST = 15
If we're solving for M, then the answer is
Using M = 15, we can now figure out the value of S.....
[5^(2S)] = (5^1)(5^15)
[5^(2S)] = (5^16)
2S = 16
S = 8
If we're solving for S, then the answer is
GMAT assassins aren't born, they're made,
Rich
Thanks a lot ! Yes the question asked for the value of m.
I didn't know that you can compare the two bases even though there is one more 5 on the right side.
Problem solved and understood. Thank you all!