We need to get the bases to match on LHS and RHS
5 ^ 21 * 4 * 11 = 2 * 10 ^ N
<=> 5 ^ 21 * 2 ^ 22 = 2 * 10 ^ N (4 = 2 ^ 2 using formula (a^b)^c = a ^ (b*c) where a= 2 b =2 c = 11)
<=> 5 ^ 21 * 2 ^ 21 * 2 = 2 * 10 ^ N (splitting 2 ^ 22 as 2 ^ 21 * (2 ^ 1 which is 2)
<=> 2 * (10) ^ 21 = 2 * 10 ^ N (5 ^ 21 and 2 ^ 21 can be combined as 10 ^ 21 using the exponent rule (a^n * b ^n = (ab)^n)
N = 21
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Source: Beat The GMAT — Problem Solving |
(5^21)(4^11) = (2)(10^n)
(5^21)(2^2)^11) = (2)(10^n)
(5^21)(2^22) = (2)(10^n)
(5^21)(2^21)(2) = (2)(10^n)
(2)(10^21) = (2)(10^n)
Eliminate the bases (2 and 10), leaving you with n = 21
ps. I think this question has been posted before, so pls 2x check as per rules of this board.
(5^21)(2^2)^11) = (2)(10^n)
(5^21)(2^22) = (2)(10^n)
(5^21)(2^21)(2) = (2)(10^n)
(2)(10^21) = (2)(10^n)
Eliminate the bases (2 and 10), leaving you with n = 21
ps. I think this question has been posted before, so pls 2x check as per rules of this board.
