Category: Logarithms

Question Number 191155 by mathlove last updated on 19/Apr/23 Answered by mahdipoor last updated on 19/Apr/23 $$log\left(xy\right)=log\left(x\right)+log\left(y\right)\Rightarrow x=a,y=1+\frac{b}{a}\Rightarrow$$$$log(a+b)=log\left(a\right)+log(1+b/a)$$$$\dots \dots ..$$$${b}=\mathrm{10}^{{B}} \:,\:{a}=\mathrm{10}^{{A}} \:,\:{c}=\mathrm{10}^{{C}}…

Question Number 124880 by WilliamsErinfolami last updated on 06/Dec/20 $$Solveforx$$$$x^{{log}_{5}3x}=12x$$ Answered by mr W last updated on 06/Dec/20 $$\left(\mathrm{log}_{\mathrm{5}}…

Question Number 59147 by Pranay last updated on 05/May/19 $$\underset{1°}{\sum ^{89°}}{log}_{2}tanr°$$ Answered by ajfour last updated on 05/May/19 $$=\mathrm{log}\:_{\mathrm{2}} \mathrm{1}=\mathrm{0}\:. \…

Question Number 121876 by oustmuchiya@gmail.com last updated on 12/Nov/20 Commented by liberty last updated on 12/Nov/20 $$\Rightarrow \sqrt{\mathrm{x}-6}=7-\sqrt{\mathrm{x}-1}$$$$\Rightarrow \mathrm{x}-6=49-14\sqrt{\mathrm{x}-1}+\mathrm{x}-1$$$$\Rightarrow 14\sqrt{\mathrm{x}-1}=54\Rightarrow \sqrt{\mathrm{x}-1}=\frac{27}{7}$$$$\Rightarrow\mathrm{x}−\mathrm{1}\:=\:\frac{\mathrm{27}^{\mathrm{2}} }{\mathrm{49}}\:;\:\mathrm{x}\:=\:\frac{\mathrm{27}^{\mathrm{2}} +\mathrm{7}^{\mathrm{2}}…

Question Number 121783 by Ar Brandon last updated on 11/Nov/20 $$\mathrm{The}\mathrm{number}\mathrm{of}\mathrm{integer}\mathrm{values}\mathrm{of}\mathrm{x}\mathrm{satisfying}$$$$\mathrm{the}\mathrm{inequality}2\mathrm{x}+1<{2\log }_2(\mathrm{x}+3)\mathrm{is}\mathrm{\_}\mathrm{\_}\mathrm{\_}.$$ Answered by TANMAY PANACEA last updated on 11/Nov/20 $$…