Question

Halle el valor de x en:

$\frac{log(12-7x)}{log x} = 2$

Answer 1

                                $\dfrac{\log(12-7x)}{\log x} = 2\\ \\ \log_x(12-7x)=2\\ \\ 12-7x=x^2\\ \\ x^2+7x-12=0\\ \\ x=\dfrac{-7\pm \sqrt{97}}{2}\\ \\ \\ \texttt{Pero... } x\ \textgreater \ 0 ~\wedge~12-7x\ \textgreater \ 0 \to x\ \textgreater \ 0\wedge x\ \textless \ \dfrac{12}{7}\\ \texttt{es decir: }0\ \textless \ x\ \textless \ \dfrac{12}{7}\\ \\ \\ \texttt{Por ende }\boxed{x=\dfrac{\sqrt{97}-7}{2}}$

Answer 2

Respuesta:

$\frac{ log(12 - 7x) }{ logx } = 2 \\ \\ \\ log_{x}(12 - 7x) = 2 \\ \\ \\ 12 - 7x = {x}^{2} \\ \\ \\ {x}^{2} + 7x - 12 = 0 \\ \\ \\ x = \frac{ - 7 ± \sqrt{97} }{2} \\ \\ \\ x = \frac{ \sqrt{97} - 7 }{2}$