Question

heeeeeelp
sabendo que log 2=0,301,log 3=0477,log 5=0,698,log 7=0,845,log 11=1,041,log 13=1,114 calcule :
1-log 28 ? 2-log 168? 3-log 143? 4-los 60
heeeeeeeeeeeelp​
alguém pode coloca o passo a passo​

Answer 1

Explicação passo-a-passo:

Utilizaremos as seguintes propriedades logarítmicas:

$log_{a} (b.c)=log_{a}b+log_{a}c\\\\log_{a}(b)^{c} =c.log_{a}b$

Sabemos que log 2=0,301, log 3=0,477, log 5=0,698, log 7=0,845,

log 11=1,041, log 13=1,114.

1)

$log 28=log(4.7)\\\\log 28=log(2^{2}.7) \\\\log 28=log 2^{2} +log 7\\\\log 28=2.log2+log7\\\\log 28=2.(0,301)+0,845\\\\log 28=0,602+0,845\\\\log 28=1,447$

2)

$log 168=log(8 .3.7)\\\\log 168=log(2^{3} .3.7)\\\\log 168=log2^{3} +log3+log7\\\\log 168=3.log2+log3+log7\\\\log 168=3.(0,301)+0,477+0,845\\\\log 168=0,903+0,477+0,845\\\\log 168=2,225$

3)

$log 143=log(11.13)\\\\log 143=log11+log13\\\\log 143=1,041+1,114=2,155\\\\log143=2,155$

4)

$log60=log(2^{2} .3.5)\\\\log60=log2^{2} +log3+log5\\\\log60=2.log2+log3+log5\\\\log60=2.(0,301)+0,477+0,698\\\\log60=0,602+0,477+0,698\\\\log60=1,777$