Question

04 – Considerando log 2 = 0,3010 e log 3 = 0,4771, calcule: log 12.

Answer 1

Explicação passo-a-passo:

Utilizaremos as seguintes propriedades logarítmicas:

$\log_{a}(b.c)= \log_{a}b+\log_{a}c$

$\log_{a}b^{c}=c.\log_{a}b$

Calculando $\log12$:

$\log12=\log(4.3)\\\\\log12=\log(2^{2}.3) \\\\\log12=\log2^{2} +\log3\\\\\log12=2.\log2+\log3\\\\\log12=2.(0,3010)+(0,4771)\\\\\log12=(0,6020)+(0,4771)\\\\\boxed{\boxed{\log12=1,0791}}$