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Question Number 121783 by Ar Brandon last updated on 11/Nov/20

$$\mathrm{The}\mathrm{number}\mathrm{of}\mathrm{integer}\mathrm{values}\mathrm{of}\mathrm{x}\mathrm{satisfying}$$ $$\mathrm{the}\mathrm{inequality}2\mathrm{x}+1<{2\log }_2(\mathrm{x}+3)\mathrm{is}\mathrm{\_}\mathrm{\_}\mathrm{\_}.$$

Answered by TANMAY PANACEA last updated on 11/Nov/20

$$$$ $$x=1LHS=3RHS=4RHS>LHS$$ $$x=-1LHS=-1RHS=2RHS>LHS$$ $$x=5LHS=11RHS=6LHS>RHS$$ $$x=13L=27R=8L>R$$ $$x=29L=59R=10L>R$$ $$\mathit{s}\mathit{o}\mathit{x}=1\mathit{a}\mathit{n}\mathit{d}-1\mathit{s}\mathit{a}\mathit{t}\mathit{i}\mathit{s}\mathit{f}\mathit{y}\mathit{t}\mathit{h}\mathit{e}\mathit{e}\mathit{q}\mathit{n}$$

Commented byAr Brandon last updated on 11/Nov/20

Thanks Sir. But there are 4 integers according to the answer guide.

Commented byDwaipayan Shikari last updated on 11/Nov/20

$$0and-2\left(Anothertwo\right)$$

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