Ensino Médio ⇒ Equação Logaritma - Iezzi Questão 306 a) Tópico resolvido

[samcinati09]

logx 3 . logx/3 + log x/81 3 = 0
Gabarito: 9 e 1/9

[petras]

samcinati09,

[tex3]\mathsf{

\frac{1}{log_3x}.\frac{1}{log_3\frac{x}{3}}+\frac{1}{log_3\frac{x}{81}}=0\\
\frac{1}{log_3x}.\frac{1}{log_3x-1}+\frac{1}{log_3x-4}=0\\
log_3x=k\\
\frac{1}{k}.\frac{1}{k-1}+\frac{1}{k-4}=0 \implies k^2-4=0\\
\therefore k =-2 \implies log_3x =-2 \implies \boxed{x = \frac{1}{9}}\\
k = 2 \implies log_3x=2 \implies \boxed{x = 9}

}[/tex3]

Código: Selecionar tudoSHIFT+Click na eq = ZOOM

[tex3]\mathsf{

\frac{1}{log_3x}.\frac{1}{log_3\frac{x}{3}}+\frac{1}{log_3\frac{x}{81}}=0\\
\frac{1}{log_3x}.\frac{1}{log_3x-1}+\frac{1}{log_3x-4}=0\\
log_3x=k\\
\frac{1}{k}.\frac{1}{k-1}+\frac{1}{k-4}=0 \implies k^2-4=0\\
\therefore k =-2 \implies log_3x =-2 \implies \boxed{x = \frac{1}{9}}\\
k = 2 \implies log_3x=2 \implies \boxed{x = 9}

}[/tex3]