log-x-x-3-7-lt-log-x-3-7-

Question Number 85694 by john santu last updated on 24/Mar/20

\log_{(\frac{x}{x - 3})} (7) < \log_{(\frac{x}{3})} (7)

Commented by jagoll last updated on 24/Mar/20

\frac{1}{\log_{7} (\frac{x}{x - 3})} < \frac{1}{\log_{7} (\frac{x}{3})}

(1) \frac{x}{x - 3} > 0 \land \frac{x}{3} > 0

\Rightarrow x > 3

(2) \log_{7} (\frac{x}{3}) < \log_{7} (\frac{x}{x - 3})

\frac{x}{3} - \frac{x}{x - 3} < 0

\frac{x (x - 6)}{3 (x - 3)} < 0 \Rightarrow x < 0 \lor 3 < x < 6

the solution \Rightarrow 3 < x < 6

Facebook Tweet Pin