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Question Number 191210 by TUN last updated on 20/Apr/23

$$2^x+2^{x+1}>3^x+3^{x+1}$$

Answered by ARUNG_Brandon_MBU last updated on 20/Apr/23

$$2^x+2^{x+1}>3^x+3^{x+1}$$ $$\Rightarrow 2^x(1+2)>3^x(1+3)$$ $$\Rightarrow 3.2^x>4.3^x\Rightarrow 2^{x-2}>3^{x-1}$$ $$\Rightarrow (x-2)\ln 2>(x-1)\ln 3$$ $$\Rightarrow (\ln 2-\ln 3)x>2\ln 2-\ln 3$$ $$\Rightarrow x<\frac{2\ln 2-\ln 3}{\ln 2-\ln 3}(\because \ln 2-\ln 3<0)$$

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