Math professionals!! What is "n" for the following question?

Question

(5 to the power of 21)x(4 to the power of 11)=2 x 10 to the power of n? What is n?? Please help!

Answer 1

n=21.
5^21 * 4^11
= 5^21 * 2^22
= 2 * (5*2)^21
=2 * 10^21

Answer 2

n=21

Answer 3

n=21. 4^11=2^22.

(5^21)(2^22)
=2(5^21)(2^21)
=2(10^21)

That gives n=21. I hope this helps, though I guess this question's already been answered be a few people....

Answer 4

(5^21)*(4^11) = 2*(10^n)
LHS = (5^21)*(2^2)^11 ( as 4 = 2^2)
= (5^21)*2^22 (as (a^b)^c = a^(bc))
= (5^21)*2*2^21( we take 2 out to make factor of 5 and 2 same)
= 2*(5^21)(2^21) (reordering)
= 2*(10)^21(as a^n*b^n = (ab)^n)
from the given condition n= 21

Answer 5

5^21 X 4^11 = 2X10^n
5^21 X 2^2(11) = 2X10^n
(5^21X2^22)/2 = 10^n
5^21 X 2^21 = 10^n
since they have th same power,
10^21 = 10^n
hence we have:
n = 21.

Answer 6

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

(5^21) * ((2^2)^11)
(5^21) * (2^(2 * 11))
(5^21) * (2^22)
(5^(21) * 2^(21)) * 2
((5 * 2)^21) * 2
2 * 10^21

ANS : n = 21

Answer 7

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

take common lograthim log 10 both side.

u get log5^21 + log4^11 = log2 + log10^n

remember loga^b = b loga and log10= 1

21log5 + 11 log 4 = log2 + n

21x 0.6990 + 11 x 0.6021 = 0.3010 + n

14.679 + 6.6231 - 0.3010 = n

so, n= 21.3021 - 0.3010

n= 21.0011

so take n as 21 , now n is 21.

Answer 8

Astrokid is right

Th