Question

2) Dados log2=0,30, log3=0,48, log5 = 0,70, quanto vale: log 1,2

Answer 1

Lembrete:

๏ $\log _b\left(a\cdot c\right)=\log _b\left(a\right)+\log _b\left(c\right)$
๏ $\log _b\left(\frac{a}{c}\right)=\log _b\left(a\right)-\log _b\left(c\right)$
๏ $\log _b\left(a^c\right)=c\cdot \log _b\left(a\right)$
--------------------------------------------------
Dados:

๏ $\log \left(2\right)=0,30$
๏ $\log \left(3\right)=0,48$
๏ $\log \left(5\right)=0,70$
--------------------------------------------------
$\log \left(1,2\right)\\\log \left(\frac{12}{10}\right)\\\log \left(\frac{3\cdot 4}{10}\right)\\\log \left(\frac{3\cdot 2^2}{10}\right)\\\log \left(3\cdot 2^2\right)-\log \left(10\right)\\\log \left(3\cdot 2^2\right)-1\\\left(\log \left(3\right)+\log \left(2^2\right)\right)-1\\\left(\log \left(3\right)+2\log \left(2\right)\right)-1\\\left(0,48+2\cdot 0,3\right)-1\\\left(0,48+0,6\right)-1\\1,06-1\\\boxed{\bold{0,06}}$