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Question Number 70003 by Maclaurin Stickker last updated on 29/Sep/19

$$Letf\left(x\right)=3^{x-1},g\left(x\right)=3^{x}andh\left(x\right)=4$$$$determinethevaluesof\mathit{x}forwhich:$$$$f\left(x\right)+g\left(x\right)⩾h\left(x\right).$$$$$$

Commented by Abdo msup. last updated on 30/Sep/19

$$f\left(x\right)+g\left(x\right)⩾4\iff 3^{x-1}+3^x⩾4\iff 3^x(3^{-1}+1)⩾4$$$$\Rightarrow (1+\frac{1}{3})3^x⩾4\Rightarrow \frac{4}{3}{3}^x⩾4\Rightarrow 3^{x-1}⩾1\Rightarrow$$$$ln\left(3^{x-1}\right)⩾0\Rightarrow (x-1)ln\left(3\right)⩾0\Rightarrow x⩾1$$

Commented by Maclaurin Stickker last updated on 30/Sep/19

$$Perfect.$$

Commented by Abdo msup. last updated on 11/Oct/19

$$thankx$$

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