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14.2: Resolver ecuaciones exponenciales y logarítmicas
https://espanol.libretexts.org/Matematicas/Precalculo_y_Trigonometria/Prec%C3%A1lculo_(Tradler_y_Carley)/14%3A_Propiedades_de_exponenciales_y_logaritmos/14.02%3A_Resolver_ecuaciones_exponenciales_y_logar%C3%ADtmicas
\[\begin{aligned} 17^{x-2}=3^{x+4} & \implies & \ln 17^{x-2}=\ln 3^{x+4} \\ & \implies & (x-2)\cdot \ln 17=(x+4)\cdot \ln 3 \\ & \implies & x\cdot \ln 17-2\cdot \ln 17=x\cdot \ln 3+4\cdot \ln 3 \\ & \... $\begin{aligned} 17^{x-2}=3^{x+4} & \implies & \ln 17^{x-2}=\ln 3^{x+4} \\ & \implies & (x-2)\cdot \ln 17=(x+4)\cdot \ln 3 \\ & \implies & x\cdot \ln 17-2\cdot \ln 17=x\cdot \ln 3+4\cdot \ln 3 \\ & \implies & x\cdot \ln 17-x\cdot \ln 3=2\cdot \ln 17+4\cdot \ln 3 \\ & \implies & x\cdot (\ln 17- \ln 3) =2\cdot \ln 17+4\cdot \ln 3 \\ & \implies & x = \dfrac{2\cdot \ln 17+4\cdot \ln 3} {\ln 17- \ln 3}\approx 5.80\end{aligned} \nonumber$

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