Help on GMAT questions

[Adevas]

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

Find N

I'm sure there is an easy way

i recognized that

5*4 is 20.

but i'm not yeilding n = 21 correct way...
2 wrongs doesn't make a right

anyhelp ?

[mikeCoolBoy]

in problems with exponents always factorize all the numbers.

In this one you have 10 and 4 which are not factorized so first do so.

10 = 2 * 5 --> 10^n = 2 ^ n * 5 ^n
4 = 2 ^ 2 ----> 4 ^11 = (2^2)^11 = 2^22

now just equal members

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

notice that 2 * 2 ^n = 2 ^(n+1)

[Adevas]

Ah thanx.

factorization.
Thats the key...

[lunarpower]

remember the general theme here: always try to get a COMMON BASE whenever you're dealing with exponentials on both sides.
if you're having difficulty discerning what that common base should be, then it's always a good idea to use primes (as is done in this problem: note that the first step is to break 4 down into 2^2 and to break 10 down into 5*2).