Question

Usando a definição, calcule o valor dos seguintes logaritmos:

a) log4 (base 64)
b) log 1/4
c) log √3 (base 9)​

Answer 1

Oie, Td Bom?!

a)

$= log_{64}(4)$

$= log_{4 {}^{3} }(4)$

$= \frac{1}{3} \: . \: log_{4}(4)$

$= \frac{1}{3} \: . \: 1$

$\boxed { = \frac{1}{3} }$

b)

$= log_{10}( \frac{1}{4} )$

$= log_{10}( \frac{1}{2 {}^{2} } )$

$= log_{10}(2 {}^{ - 2} )$

$= - 2 log_{10}(2)$

$\boxed {≈ - 0,602...}$

c)

$= log_{9}( \sqrt{3} )$

$= log_{3 {}^{2} }( 3{}^{ \frac{1}{2} } )$

$= \frac{ \frac{1}{2} }{2} \: . \: log_{3}(3)$

$= \frac{ \frac{1}{2} }{2} \: . \: 1$

$= \frac{ \frac{1}{2} }{2}$

$= \frac{1}{2} \: . \: 2$

$= \frac{1}{2} \: . \: \frac{1}{2}$

$\boxed { = \frac{1}{4} }$

Att. Makaveli1996