Question

Considerando
Log2 = 0,3
Log3 = 0,5
Log5 = 0,7
Determine o valor de:
A) log 1,2
B) (log 1,5)^2
C) log√0,3

Answer 1

Boa tarde!

A)

$log 1,2 = log(\frac{12}{10}) = log12 - log10 = log12 - 1 = log(3.2.2) - 1 = log3 + log2 + log2 - 1 = 0,5 + 0,3 + 0,3 - 1 = 1,1 - 1 = 0,1$

B)

$(log1,5)^{2} = [log(\frac{15}{10})]^{2} = (log15 - log10)^{2} = [log(5.3) -1]^{2} = (log5 + log3 -1)^{2} = 0,7+0,5-1 = 1,2 -1 = 0,2$

C)

$log\sqrt{0,3} = log0,3^{\frac{1}{2}} = \frac{1}{2}.log0,3 = \frac{1}{2}.log(\frac{3}{10}) = \frac{1}{2}.(log3 - log10) = \frac{1}{2}.(0,5 - 1) = \frac{1}{2}.-0,5 = -0,25$

Espero ter ajudado!