Question

Considerando ㏒₂≈0,30,㏒₃≈0,48 e ㏒₅≈0,70 calcule: ㏒²⁰

Answer 1

Lembrando que:
$\log_{b}{(a \cdot c)} = \log_{b}a + \log_{b}c \\ e \\\log_{b}a^c = c \cdot \log_{b}a$

$\log20 = \log(5 \cdot 4) = \log5 + \log4 = \\ \log5 + \log {2}^{2} = \log5 + 2 \cdot \log2 = \\ 0,70 + 2 \cdot 0,30 = 0,70 + 0,60 = 1,30$