Verified answer

x = 4^12 * 5^20

x = 2^12* (2^12 *5^12) * 5^8

x = (2.5)^12 * 2^12 * 5^8

x = 10^12 * 10^8 * 2^4

x = 16. 10^20 --> 22 algarismos

y = 4^14 * 5^18

y = 2^14 * (2^14 * 5^14) * 5^4

y = (2.5)^14 * (2.5)^4 * 2^10

y = 10^18 * 1024 --> 22 algarismos

alternativa A

x = 4¹² * 5²⁰

logx = 12 log4 + 20 log5 = 12 log2² + 20 log10/2 = 24 log2 + 20(log10 - log2)

logx = 24 log2 + 20 - 20 log2 = 4log2 + 20

logx = 1,20 + 20 = 21,20 --> x tem 22 algarimos

a = 22

y =4¹⁴ * 5¹⁸

logy = 14 log2² + 18 (log10/2) = 28log2 + 18(log10 - log2) = 28log2 + 18 - 18 log2

logy = 10log2 + 18

y = 3,01 + 18 = 21,01 --> y tem 22 algarismos

b = 22

resposta (a)

x = 4^12 * 5^20 = 2^24 * 5^20 = 2^(6+18) * 5^(2+18) = 64*2^18*25*5^18 = 1600*10^18

y = 4^14 * 5^18 = 2^28 * 5^18 = 2^(10+18) * 5^18 = 1024*2^18*5^18 = 1024*10^18

a = b = 4 + 18 = 22 algarismos

pronto