Question

O logaritmo de 8⁴ na base 8³ é?
A)4/3 B)3/4 C)12 D)7 E)1
Precisa do cálculo!!!

Answer 1

Resposta:

$\boxed{\mathtt{A}}$

Explicação passo-a-passo:

$\\ \displaystyle \mathsf{\log_{8^3} 8^4 =} \\\\ \mathsf{\frac{1}{3} \cdot 4 \cdot \log_8 8 =} \\\\ \mathsf{\frac{1}{3} \cdot 4 \cdot 1 =} \\\\ \boxed{\boxed{\mathsf{\frac{4}{3}}}}$

Propriedades utilizadas:

$\\ \displaystyle \mathtt{\bullet \qquad \qquad \log_a b^c = c \cdot \log_a b} \\\\ \mathtt{\bullet \qquad \qquad \log_{a^d} b = \frac{1}{d} \cdot \log_a b} \\\\\\ \mathtt{\forall \, 1 \neq a, b, c > 0 \, e \, d \neq 0.}$