Question

como se calcula o log 2raiz3 elevado a 144?(exercício 11)

Answer 1

 Olá Mario,

$\log_{2\sqrt{3}}144=\\\\\\\frac{\log_{10}144}{\log_{10}2\sqrt{3}}=\\\\\\\frac{\log144}{\log\sqrt{2^2\cdot3}}\\\\\\\frac{\log12^2}{\log\sqrt{12}}=\\\\\\\frac{\log12^2}{\log12^{\frac{1}{2}}}=\\\\\\\frac{2\cdot\log12}{\frac{1}{2}\cdot\log12}=\\\\\\2\div\frac{1}{2}=\\\\\\2\cdot\frac{2}{1}=\\\\\\\boxed{4}$