Question

Usando as aproximações log2 = 0,301, log 3=0,477 e log7= 0,845determine o valor do logaritmo log de 20 na base5:
a)igual a 1,785
b)igual a 1,965
c)igual a 1,861
d)igual a 1,698

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{log\:2 = 0,301}$

$\mathsf{log\:3 = 0,477}$

$\mathsf{log\:7 = 0,845}$

$\mathsf{log_5\:20 = \dfrac{log\:20}{log\:5}}$

$\mathsf{log_5\:20 = \dfrac{log\:(2.10)}{log\:\dfrac{10}{2}}}$

$\mathsf{log_5\:20 = \dfrac{log\:2+ log\:10}{log\:10 - log\:2}}$

$\mathsf{log_5\:20 = \dfrac{0,301 + 1}{1 - 0,301}}$

$\mathsf{log_5\:20 = \dfrac{1,301}{0,699}}$

$\boxed{\boxed{\mathsf{log_5\:20 = 1,861}}}}\leftarrow\textsf{letra C}$