Question

sendo log 2=a e log 3 = b, calculei log


$\sqrt[3]{12}$
em função de a e b

Answer 1

Olá, tudo bem?

$\log\sqrt[3]{12}=\\\\\log\sqrt[3]{2^2\cdot 3}=\\\\\log\left(2^{\frac{2}{3}}\cdot 3^{\frac{1}{3}}\right)=\\\\\log(2^{\frac{2}{3}})+\log(3^{\frac{1}{3}})=\\\\\dfrac{2}{3}\log(2)+\dfrac{1}{3}\log(3)=\\\\\boxed{\dfrac{2a+b}{3}}$

É isso!! :)