Question

ME AJUDEM POR FAVOR !!!!
MACK- SP Se ㏒a 2 = m e ㏒a 3 = n, então ㏒1/a 2/3 vale:

( lê-se: log de 2 na base igual a m; log de 3 n bse a igual a n; log de 2/3 na base 1/a vale:)

a) 1
b) 0
c) m-n
d) n-m
e) mn

Answer 1

Olá Karina!

$\\ \displaystyle \mathsf{\log_{\frac{1}{a}} \frac{2}{3} =} \\\\ \mathsf{\log_{\frac{1}{a}} 2 - \log_{\frac{1}{a}} 3 =} \\\\ \mathsf{\log_{a^{- 1}} 2 - \log_{a^{- 1}} 3 =} \\\\ \mathsf{\frac{1}{- 1} \cdot \log_a 2 - \frac{1}{- 1} \cdot \log_a 3 =} \\\\ \mathsf{- \log_a 2 + \log_a 3 =} \\\\ \mathsf{- m + n =} \\\\ \boxed{\mathsf{n - m}}$

A saber,

$\mathbf{\log_{a^n} b = \frac{1}{n} \cdot \log_a b}$