Exponents, power manipulation

[kittenko]

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


Thank you very much!

[Brent@GMATPrepNow]

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@GMATPrepNow]

(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