Question

Sabendo que log5 2= 0,43, Log 5 3 = 0,68, Calcule
a) log5 6
B) log5 2/3
c) log5 8
D) log5 24

Answer 1

E aí véio,

use as propriedades de log a seguir, em seguida substitua os valores de log dados:

$log(bc)~\to~log(b\cdot c)~\to~logb+logc\\\\ log \dfrac{b}{c}~\to~logb-logc\\\\ logb^k=c~\to~k\cdot logb$

________________

$log_56=log_5(2\cdot3)\\ log_56=log_52+log_53\\ log_56=0,43+0,68\\\\ \large\boxed{\boxed{\boxed{log_56=1,11}}}.\\.\\\\ log_5 \dfrac{2}{3}=log_52-log_53\\\\ log_5 \dfrac{2}{3}=0,43-0,68\\\\ \boxed{\boxed{\boxed{log_5 \dfrac{2}{3}=-0,25}}}.\\.\\\\ log_58=log_52^3\\ log_58=3\cdot log_52\\ log_58=3\cdot0,43\\\\ \large\boxed{\boxed{\boxed{log_58=1,29}}}.\\.\\\\ log_524=log_5(2^3\cdot3\\ log_524=log_52^3+log3\\ log_524=3\cdot log2+log3\\ log_524=3\cdot0,43+0,68\\\\ \large\boxed{\boxed{\boxed{log_524=1,97}}}\\.$

vlw (y)