Question

Dados log 2=0,3 e log 3 = 0,48,
calcule:
log6
log30
log8
log raiz de 3
log base 2 logaritimando 3
log base 9 logaritimando 32
log base 3 logaritimando 2
log base 81 logaritimando 16

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{a)\:log\:6 = log\:(2.3) = log\:2 + log\:3 = 0,3 + 0,48 = 0,78}$

$\mathsf{b)\:log\:30 = log\:(3.10) = log\:3 + log\:10 = 0,48 + 1 = 1,48}$

$\mathsf{c)\:log\:8 = log\:2^3 = 3\:log\:2 = 3(0,30) = 0,90}$

$\mathsf{d)\:log\:\sqrt{3} = log\:3^{\frac{1}{2}} = \frac{1}{2}\:.\:log\:3 = 0,24}$

$\mathsf{e)\:log_2\:3 = \frac{log\:3}{log\:2} = \frac{0,48}{0,3} = 1,6}$

$\mathsf{f)\:log_9\:32 = \frac{log\:32}{log\:9} = \frac{log\:2^5}{log\:3^2} = \frac{5\:log\:2}{2\:log\:3} = \frac{5(0,3)}{2(0,48)} = \frac{1,5}{0,96} = 1,56}$

$\mathsf{g)\:log_3\:2 = \frac{log\:2}{log\:3} = \frac{0,3}{0,48} = 0,63}$

$\mathsf{h)\:log_{81}\:16 = log_{3^4}\:2^4 = log_3\:2 = \frac{log\:2}{log\:3} = \frac{0,3}{0,48} = 0,63}$