Respuestas

2012-05-27T22:01:21+02:00

1. \begin{gathered} {\log _3}\left( {2x + 5} \right) = 2 \hfill \\ \Rightarrow \frac{{\log \left( {2x + 5} \right)}}{{\log 3}} = 2 \hfill \\ \Rightarrow \log \left( {2x + 5} \right) = 2\log 3 = \log {3^2} \hfill \\ \Rightarrow \log \left( {2x + 5} \right) = \log 9 \hfill \\ \Rightarrow 2x + 5 = 9 \hfill \\ \Rightarrow 2x = 4 \hfill \\ \Rightarrow x = 2 \hfill \\ \end{gathered}

 

3. \[\begin{gathered} \log \left[ {\left( {x - 1} \right)\left( {x + 5} \right)} \right] = 2 \hfill \\ \Rightarrow \log \left[ {\left( {x - 1} \right)\left( {x + 5} \right)} \right] = \log 100 \hfill \\ \Rightarrow \left( {x - 1} \right)\left( {x + 5} \right) = 100 \hfill \\ \Rightarrow {x^2} + 4x - 5 = 100 \hfill \\ \Rightarrow {x^2} + 4x - 105 = 0 \hfill \\ \Rightarrow x = - 2 + \sqrt {109} \vee x = - 2 - \sqrt {109} \hfill \\ \end{gathered}

 

las otras se hacen igual...