log-9-x-7-2-log-3-4-x-2-log-3-4-x-7-2-

Question Number 92319 by jagoll last updated on 06/May/20

\log_{9} (x + \frac{7}{2}) . \log_{3 / 4} (x^{2}) ⩾

\log_{3 / 4} (x + \frac{7}{2})

Commented by john santu last updated on 06/May/20

{\begin{cases} x + \frac{7}{2} > 0 \Rightarrow x > - \frac{7}{2} \\ x^{2} > 0 \Rightarrow x \neq 0 \end{cases}

\frac{1}{2} \log_{3} (x + \frac{7}{2}) . \frac{\log_{3} (x^{2})}{\log_{3} (\frac{3}{4})} ⩾ \frac{\log_{3} (x + \frac{7}{2})}{\log_{3} (\frac{3}{4})}

\log_{3} (x + \frac{7}{2}) (\frac{1}{2} \log_{3} (x^{2}) - 1) ⩽ 0

(- \frac{7}{2}, - 3] \cup [- \frac{5}{2}, 0) \cup (0, 3)

Commented by jagoll last updated on 06/May/20

Is this the cut step? why so short?

Commented by jagoll last updated on 06/May/20

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