Question

considerando log 2=0,3 e log 7=0,85,calcule: logaritmo 14 na base 8

Answer 1

Dado log2=0,3 e log7=0,85, calcular log14 base 8 

Log₈14=X ⇔ método logₓY =a  ⇔  Xᵃ=Y

Log₈14=X
8ˣ=14
xlog8=log14
x.(log2³)=Log7.2
x.(3.log2)=Log7+Log2

substituindo os valores de log 

x.(3.0,3)=0,85+0,3
x=1,15/0,9
X=1,27 

Espero ter ajudado! 

Answer 2

Propriedades:

๏ $\mathsf{\log _b\left(a\right)=\dfrac{\log _c\left(a\right)}{\log _c\left(b\right)}}$

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

๏ $\mathsf{\log \left(2\right)\approx 0,3}$
๏ $\mathsf{\log \left(7\right)\approx 0,85}$
---------------
Resolução:

$\mathsf{\log _8\left(14\right)}\\\\\\\mathsf{\dfrac{\log \left(14\right)}{\log \left(8\right)}}\\\\\\\mathsf{\dfrac{\log \left(2\cdot 7\right)}{\log \left(2^3\right)}}\\\\\\\mathsf{\dfrac{\log \left(2\right)+\log \left(7\right)}{3\cdot \log \left(2\right)}}\\\\\\\mathsf{\dfrac{0,3+0,85}{3\cdot 0,3}}\\\\\\\mathsf{\dfrac{1,15}{0,9}}\\\\\\\mathsf{\dfrac{115}{90}}\\\\\\\boxed{\mathsf{\dfrac{115}{90}\:ou\:1,2\overline{7}}}\: \: \checkmark$