log-2-x-log-1-x-1-2-0-x-

Question Number 12489 by Joel577 last updated on 23/Apr/17

\log_{2} x + \log_{1 / x} \frac{1}{2} ⩾ 0

x = ?

Answered by mrW1 last updated on 23/Apr/17

\frac{\ln x}{\ln 2} + \frac{\ln (\frac{1}{2})}{\ln (\frac{1}{x})} ⩾ 0

\frac{\ln x}{\ln 2} + \frac{\ln 2}{\ln x} ⩾ 0

\frac{{(\ln x)}^{2} + {(\ln 2)}^{2}}{(\ln 2) (\ln x)} ⩾ 0

(\ln 2) (\ln x) > 0

\ln x > 0

\Rightarrow x > 1

Commented by Joel577 last updated on 24/Apr/17

t h a n k y o u v e r y m u c h

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