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Question-70108




Question Number 70108 by naka3546 last updated on 01/Oct/19
Answered by MJS last updated on 01/Oct/19
((1/4))^x >3^(36) ((2/3))^(18x)   (−2ln 2)x>36ln 3 +18(ln 2 −ln 3)x  (18ln 3 −20 ln 2)x>36ln 3  x>((18ln 3)/(9ln 3 −10ln 2))≈6.68970287
$$\left(\frac{\mathrm{1}}{\mathrm{4}}\right)^{{x}} >\mathrm{3}^{\mathrm{36}} \left(\frac{\mathrm{2}}{\mathrm{3}}\right)^{\mathrm{18}{x}} \\ $$$$\left(−\mathrm{2ln}\:\mathrm{2}\right){x}>\mathrm{36ln}\:\mathrm{3}\:+\mathrm{18}\left(\mathrm{ln}\:\mathrm{2}\:−\mathrm{ln}\:\mathrm{3}\right){x} \\ $$$$\left(\mathrm{18ln}\:\mathrm{3}\:−\mathrm{20}\:\mathrm{ln}\:\mathrm{2}\right){x}>\mathrm{36ln}\:\mathrm{3} \\ $$$${x}>\frac{\mathrm{18ln}\:\mathrm{3}}{\mathrm{9ln}\:\mathrm{3}\:−\mathrm{10ln}\:\mathrm{2}}\approx\mathrm{6}.\mathrm{68970287} \\ $$

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