Question

determine valor de log x:


8
18
11
15
10
​

Answer 1

$log_{_x}\,\frac{a^2.b^3}{\sqrt[3]{c}}~=\\\\\\Utilizando~a~propriedade~do~logaritmo~do~quociente:\\\\\\=~log_{_x}\,(a^2.b^3)~-~log_{_x}\,\sqrt[3]{c}~=\\\\\\Utilizando~a~propriedade~do~logaritmo~do~produto:\\\\\\=~\left(log_{_x}\,a^2~+~log_{_x}b^3\right)~-~log_{_x}\,\sqrt[3]{c}~=\\\\\\Transformando~o~radical~\sqrt[3]{c}~em~expoente~fracionario:\\\\\\=~\left(log_{_x}\,a^2~+~log_{_x}b^3\right)~-~log_{_x}\,c^{\frac{1}{3}}~=\\\\\\Utilizando~a~propriedade~do~logaritmo~do~expoente:$

$=~\left(2.log_{_x}\,a~+~3.log_{_x}b\right)~-~\frac{1}{3}.log_{_x}\,c~=\\\\\\Substituindo~os~logaritmos~pelos~valores~fornecidos~no~enunciado:\\\\\\=~\left(2~.~2~+~3~.~3\right)~-~\frac{1}{3}~.~6~=\\\\\\=~\left(4~+~9\right)~-~2~=\\\\\\=~13~-~2~=\\\\\\=~\boxed{11}$

Resposta: 11