Question

Calcule os logaritmos abaixo (é possível utilizar a calculadora, mas esta somente
calcula logaritmos na base 10:

Answer 1

Resposta:

a) 2

b) 2,5

c) 3

Explicação passo-a-passo:

• Desenvolvendo os logaritmos:

(A)

$log_{25}(625)\\\\log_{25}(25^{2})\\\\2*log_{25}(25)\\\\2*1\\\\2$

(B)

$log_{16}(1024)\\\\log_{2^{4}}(2^{10})\\\\\frac{10}{4} *log_{2}(2)\\\\\frac{10}{4}*1\\\\\frac{10}{4}\\\\\frac{5}{2}\\\\2,5$

(C)

$log_{100}(1.000.000)\\\\log_{10^{2}}(10^{6})\\\\\frac{6}{2}*log_{10}(10)\\\\\frac{6}{2}*1\\\\3$

Espero ter ajudado!

Answer 2

a)$log_{25}625 = 2,$ pois 25²=625

b)$log_{16}1024 = log_{2^4} 2^10 = 10*\frac{1}{4} =log_{2} 2=\frac{5}{2}$

c)$log_{100}1000000=log_{10^2}10^6=6*\frac{1}{2}log_{10}10 =  \frac{6}{2}=3$