Question

SOCORROOOO, URGENTE

41. Pela definição de cologaritmo, calcule:
a) colog2 8
b) colog3 (1/81)
c) colog10 0,001
d) colog2 2 raiz de 2

ME AJUDEM PFV VALE 100 PONTOOOS
PRA AGORA

Answer 1

Resposta:

Definição de cologaritmo.

$\red{colog_{b}(a)\:=\:-\:log_{b}(a)}$

$co log_{2}(8) = x \\ \\ - log_{2}(8) = x \\ \\ - ({2}^{x} = 8) \\ \\ - ( {2}^{x} = {2}^{3} ) \\ \\ x = - (3) \\ \\ \red{x = 3}$

ou

$log_{2}( { \frac{1}{8} } ) = x \\ \\ {2}^{x} = \frac{1}{8} \\ \\ {2}^{x} = \frac{1}{ {2}^{3} } \\ \\ {2}^{x} = {2}^{ - 3} \\ \\ \blue{x = - 3}$

b)

$co log_{3}( \frac{1}{81} ) = x \\ \\ - log_{3}( \frac{1}{81} ) = x \\ \\ -( {3}^{x} = \frac{1}{ {3}^{4} } ) \\ \\ - ( {3}^{x} = {3}^{ - 4} ) \\ \\ x = - ( - 3) \\ \\ \red{x = 3}$

c)

$co log_{10}(0.001) = x \\ \\ - log_{10}( {10}^{ - 3} ) = x \\ \\ - ( {10}^{x} = {10}^{ - 3} ) \\ \\ x = - ( - 3) \\ \\ \red{x = 3}$

d)

$co log_{2}( \frac{ \sqrt{2} }{2} ) = x \\ \\ - log_{2}( \frac{ \sqrt{2} }{2} ) = x \\ \\ - ( {2}^{x} = \frac{ \sqrt{2} }{2} ) \\ \\ - ( {2}^{x} = \frac{ {2}^{ \frac{1}{2} } }{2} ) \\ \\ - ( {2}^{x} = {2}^{ \frac{1}{2} - 1} ) \\ \\ - ( {2}^{x} = {2}^{ - \frac{1 }{2} } ) \\ \\ x = - ( - \frac{1 }{2} ) \\ \\ \red{x = \dfrac{1}{2} }$

Bons Estudos!