Question

Sabendo que log₁₂ 5=a, calcue, em função de a, o valor dos seguintes logaritmos:
a) log₅ 12
b) log₂₅ 12
c) log₅ 60

Answer 1

Mudança de bases.

$log\ _5\ 12 = \frac{log\ _1_2\ 12}{log\ _1_2\ 5}\\\\\ \boxed{log\ _5\ 12 = \frac{1}{a}}$

$log\ _2_5\ 12 = \frac{log\ _1_2\ 12}{log\ _1_2\ 25} = \frac{1}{log\ _1_2\ 5^2}=\frac{1}{2a}\\\\\ \boxed{log\ _2_5\ 12 = \frac{1}{2a}}$

$log\ _5\ 60 = \frac{log\ _1_2\ 60}{log\ _1_2\ 5} = \frac{log\ _1_2\ 12*5}{a} = \frac{log\ _1_2\ 12+log\ _1_2\ 5}{a} = \frac{1+a}{a}\\\\ \boxed{log\ _5\ 60 =\frac{1+a}{a}}$

Answer 2

Resposta:

a) log5 (12) = log12 (12)/ log12 (5) = 1/a

b) log25 (12) = log12 (12)/ log12 (5²) = 1/2a

c) log5 (60) = log5 (12) + log5 (5) = 1 + a/a