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mathmath333
 one year ago
Prove.
mathmath333
 one year ago
Prove.

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mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0\(\large \color{black}{\begin{align} & 1.)\ \normalsize \text{If }\ a>1\ \text{and}\ \log_{a}x_{1}>\log_{a}x_{2}, \hspace{.33em}\\~\\ & \normalsize \text{then}\ x_{1}>x_{2} \hspace{.33em}\\~\\ & 2.)\ \normalsize \text{If }\ a<1\ \text{and}\ \log_{a}x_{1}>\log_{a}x_{2}, \hspace{.33em}\\~\\ & \normalsize \text{then}\ x_{1}<x_{2} \hspace{.33em}\\~\\ \end{align}}\)

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.5case 1) we can write: \[\Large \begin{gathered} {\log _a}{x_1}  {\log _a}{x_2} > 0 \hfill \\ {\log _a}\left( {\frac{{{x_1}}}{{{x_2}}}} \right) > 0 \Rightarrow \frac{{{x_1}}}{{{x_2}}} > 1 \hfill \\ \end{gathered} \]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.5case 2) we have \[\Large \begin{gathered} {\log _a}{x_1}  {\log _a}{x_2} > 0 \hfill \\ {\log _a}\left( {\frac{{{x_1}}}{{{x_2}}}} \right) > 0 \Rightarrow \frac{{{x_1}}}{{{x_2}}} < 1 \hfill \\ \end{gathered} \]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.5please keep in mind these graphs: dw:1437675202816:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0all youre doing is proving that theyre monotonic ...
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