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Question Number 121778 by Ar Brandon last updated on 11/Nov/20

$$\mathrm{The}\mathrm{number}\mathrm{of}\mathrm{integers}\mathrm{satisfying}\mathrm{the}\mathrm{inequality}$$$$3^{\left(5/2\right){\log }_3(12-3\mathrm{x})}-3^{{\log }_2\mathrm{x}}>83\mathrm{is}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}$$

Commented by 676597498 last updated on 11/Nov/20

$$\mathrm{is}\mathrm{it}.....-3^{{\log }_3\mathrm{x}}\mathrm{or}...-3^{{\log }_2\mathrm{x}}$$

Commented by Ar Brandon last updated on 11/Nov/20

$${\mathrm{it}}^{\prime }\mathrm{s}...-3^{{\log }_2\mathrm{x}}$$

Answered by floor(10²Eta[1]) last updated on 11/Nov/20

$$12-3\mathrm{x}>0\Rightarrow \mathrm{x}⩽3$$$$\mathrm{x}>0\Rightarrow \mathrm{x}⩾1$$$$\Rightarrow 1⩽\mathrm{x}⩽3$$$$\mathrm{only}\mathrm{x}=1\mathrm{and}\mathrm{x}=2\mathrm{works}$$

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