please show work. TIA

[daretodream]

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

[harsh.champ]

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

R.H.S.= (2) x (2)^n x (5)^n
=[(2)^(n+1)] x 5^n

L.H.S. = 5^21 X 2^22

So, comparing exponents we get n=21

[ajith]

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

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

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

5^21* 2^22 = 2*10^n

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

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

2* (10)^21 =2*10^n

n =21

[shashank.ism]

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

5^21 x 4^11 = 2 x 10^n
It is simple question of equation powers of similar base as discussed in some earlier post
--> 5^21 x 2^22 = 2 x (5x2)^n
--> 5^21 x 2^22 = 2^(n+1) x 5^n

[spoiler]so n = 21 ans[/spoiler]

[thephoenix]

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

LHS=5^21 * 2^22
RHS=2*(2*50)^n=2^(n+1) * 5^n

when LHS=RHS----> n=21