Category: Logarithms

Question Number 3160 by prakash jain last updated on 06/Dec/15 $$\mathrm{Prove}\mathrm{that}e=\underset{n=0}{\sum ^{\mathrm{\infty }}}\frac{1}{n!}\mathrm{is}\mathrm{irrational}.$$ Answered by Yozzi last updated on 06/Dec/15 $${Fourier}^{\prime }sProof$$$${Suppose}\:{for}\:{contradiction}\:{that}…

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…

Question Number 133936 by liberty last updated on 25/Feb/21 $$\log {}_{\mathrm{x}+8}({\mathrm{x}}^2-3\mathrm{x}-4)<2.\log {}_{{(4-\mathrm{x})}^2}(\mid \mathrm{x}-4\mid )$$ Answered by EDWIN88 last updated on 25/Feb/21 $$\:\mathrm{log}\:_{\mathrm{x}+\mathrm{8}} \left(\mathrm{x}^{\mathrm{2}}…

Question Number 1880 by alib last updated on 20/Oct/15 $$Solve$$$$$$$$1){(sin2x+\sqrt{}3cos2x)}^2=2-2cos(\frac{2\pi }{3}-x)$$$$2)cosx-cos2x=sin3x$$$$$$$$3)sin(15°+x)+cos(45°+x)+\frac{1}{2}=0$$$$\left.\mathrm{4}\right)\:{tan}\:\left(\mathrm{70}°+{x}\right)\:+\:{tan}\:\left(\mathrm{20}°−{x}\right)\:=\:\mathrm{2} \…

Question Number 66413 by hmamarques1994@gmail.com last updated on 14/Aug/19 $$$$$$\sqrt{8+{\mathbf{log}}_6(\mathbf{x}!)}+\sqrt{17-{\mathbf{log}}_{\mathbf{x}!}\left(6\right)}=7$$$$$$ Answered by MJS last updated on 14/Aug/19…