Question

Sabendo que log⁡ 2=m e log⁡3=n, calcule log⁡∛72 em função de m e n. *
1 ponto
a) (2m+3n)/3
b) (3m+2n)/2
c) (3m+2n)/3
d) (3m+3n)/3
e) (3m+n)/3

Answer 1

$\displaystyle \sf \log2=m \ \ , \ \ \log 3 = n \\\\ \log\sqrt[3]{72} =\ ?\\\\\ \log\sqrt[3]{72} \to \log\left(72\right)^{\displaystyle \frac{1}{3}} \to \frac{1}{3}\cdot \log 72 \\\\\\\ \frac{1}{3}\cdot \log \left(8\cdot 9\right) \to \frac{1}{3}\cdot \left ( \log 8+\log 9 \right) \\\\\\ \frac{1}{3}\cdot \left ( \log 8+\log 9 \right) \to \frac{1}{3}\cdot \left(\log 2^3+\log 3^2\right) \\\\\\ \frac{1}{3}\cdot \left(\log 2^3+\log 3^2\right) \to \frac{1}{3}\cdot \left(3\log 2+2\log 3 \right)$

$\displaystyle \sf \frac{1}{3}\cdot \left(3\log 2+2\log 3 \right) \to \frac{1}{3}\cdot \left(3\cdot m +2\cdot n \right) \\\\\\ \huge\boxed{\frac{\ \sf \left(3\cdot m +2\cdot n \right)}{3}\ }\checkmark$

letra c