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Question Number 68618 by Rio Michael last updated on 14/Sep/19

$$solveforxthefollowingequations$$$$a)log{x}^3-2log{x}^2+2logx+2log\sqrt{x}=3$$$$b){log}_{x}24-3{log}_{x}4+2{log}_{x}3=-3$$

Answered by Rasheed.Sindhi last updated on 14/Sep/19

$$a)log{x}^3-2log{x}^2+2logx+2log\sqrt{x}=3$$$$b){log}_{x}24-3{log}_{x}4+2{log}_{x}3=-3$$$$$$$$\mathrm{a})\Rightarrow 3\log \mathrm{x}-4\mathrm{logx}+2\mathrm{logx}+\mathrm{logx}=3$$$$2\log \mathrm{x}=3$$$$\mathrm{x}=\mathrm{Antilog}\left(\frac{3}{2}\right)={10}^{\frac{3}{2}}=\sqrt{1000}=10\sqrt{10}$$$$b){log}_{x}24-3{log}_{x}4+2{log}_{x}3=-3$$$${\log }_{\mathrm{x}}24-{\log }_{\mathrm{x}}{4}^3+{\log }_{\mathrm{x}}{3}^2=-3$$$${\log }_{\mathrm{x}}\left(\frac{24\times 9}{64}\right)=-3$$$${\log }_{\mathrm{x}}\left(\frac{27}{8}\right)=-3$$$${\mathrm{x}}^{-3}=\frac{27}{8}={\left(\frac{3}{2}\right)}^3={\left(\frac{2}{3}\right)}^{-3}$$$$\mathrm{x}=\frac{2}{3}$$

Commented by Rio Michael last updated on 15/Sep/19

$$thankssir$$

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