Question

Dados log 2 = 0,30, log 3 = 0,47 e log 5 = 0,70, calcule o valor dos logarítimos utilizando a mudança de base.

A)log 3 base 2
B)log 3 base 5
C)log 9 base 8
D)log 5 base 100

Answer 1

A)

$log_{2}3$

$⇩$

utilizando mudança de base:

$\large{\frac{ log_{10}3 }{ log_{10}2} }$

$⇩$

substituindo os valores dados:

$\frac{0,47}{0,30}$

$⇩$

$\red { \large{ \bold{ 1,5666...}}}$

.......

.......

B)

$log_{5}3$

$⇩$

$\large{\frac{ log_{10}3 }{ log_{10}5 } }$

$⇩$

$\frac{0 ,47}{0, 70}$

$⇩$

$\red{ \bold{ \large{0,6714...}}}$

......

......

......

C)

$log_{8}9$

$⇩$

$\frac{ log_{10}9 }{ log_{10}8 }$

$⇩$

$\\ \frac{ log_{10} {3}^{2} }{ log_{10} {2}^{3} }$

$⇩$

$\large{ \frac{2. log_{10}3 }{3. log_{10}2} }$

$⇩$

$\large{\frac{2 \: . \: 0 , \: 47}{3 \: . \: 0 ,30 } }$

$⇩$

$\frac{0 ,94 }{0 ,90\: }$

$⇩$

$\red{ \bold{ \large{1,0444...}}}$

......

......

D)

$log_{100}5$

$⇩$

$\large{\frac{ log_{10}5 }{ log_{10}100 } }$

$⇩$

$\large{ \frac{ log_{10}5}{ log_{10} {10}^{2} } }$

$⇩$

$\frac{ log_{10}5}{ 2 \: . \: log_{10}10}$

$⇩$

$\large{\frac{ log_{10}5}{ 2 \: . \: 1} }$

$⇩$

$\frac{0 ,70}{2}$

$⇩$

$\red{ \bold{ \large{0,35}}}$