Question

preciso urgenteeee

sabendo-se que 2^p=5, podemos concluir que log2 100 é igual a:

a) 2/p
b)2p
c)2+p^2
d)2+2p
e)2+2p/p

Answer 1

$2^p = 5 \\\\ p = log_2(5) \\\\ log_2(100) = log_2(10^2) \\\\ log_2(100) = 2log_2(10) \\\\ log_2(100) = 2log_2(2 \times 5) \\\\ log_2(100) = 2( log_2(2) \times log_2(5) )\\\\ log_2(100) = 2( 1 + log_2(5)) \\\\ log_2(100) = 2(1 + p) \\\\ \boxed{log_2(100) = 2 + 2p}$

Resposta: letra d)