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




Question Number 182702 by CrispyXYZ last updated on 13/Dec/22
log_2 (x+1)−x>0
$$\mathrm{log}_{\mathrm{2}} \left({x}+\mathrm{1}\right)−{x}>\mathrm{0} \\ $$
Commented by mr W last updated on 13/Dec/22
at x=0 and x=1: log_2  (x+1)=x  ⇒−1<x<0 ∨ 1<x<+∞
$${at}\:{x}=\mathrm{0}\:{and}\:{x}=\mathrm{1}:\:\mathrm{log}_{\mathrm{2}} \:\left({x}+\mathrm{1}\right)={x} \\ $$$$\Rightarrow−\mathrm{1}<{x}<\mathrm{0}\:\vee\:\mathrm{1}<{x}<+\infty \\ $$

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