Question

64) Calcule o valor de: log₃ 1 + log₄ 4 - log₅ 5⁻⁶

Answer 1

log₃ 1 = 0
log₄ 4 = 1
log₅ 5⁻⁶ = -6x1= -6

log₃ 1 + log₄ 4 - log₅ 5⁻⁶
0 + 1 - (- 6)
= 7

Answer 2

Propriedades de log : 

$\boxed{\ log_a\ b=\ x\ \ \ \ \ -\ \textgreater \ a^{x}=b\ }$

Resolvendo ... 

$log_3\ 1=x\\\\log_4\ 4=y\\\\log_5\ 5^{-6}=z\\\\\\assim:\\\\log_3\ 1\ +\ log_4\ 4\ -\ log_5\ 5^{-6}\ =\ \boxed{x+y-z}$

Encontrando a valor de cada um ... 

$log_3\ 1=x\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ log_4\ 4=y\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ log_5\ 5^{-6}=z\\\\ \ 3^{x}=1\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 4^{y}=4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 5^{z}=5^{-6}\\\\3^{x}=3^{0}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 4^{y}=4^{1}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 5^{z}=5^{-6}\\\\\boxed{x=0}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \boxed{y=1}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \boxed{z=-6}$

voltando a equação ... 

$x+y-z\\\\\\0+1-(-6)\\\\1+6=\boxed{7}\\\\\\Assim\ :\\\\\\\boxed{\boxed{\boxed{log_3\ 1\ +\ log_4\ 4\ -\ log_5\ 5^{-6}\ =\ 7\ \ }}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ok$