Category: Logarithms

Question Number 10186 by prakash jain last updated on 29/Jan/17 $$\mathrm{Prove}$$$$\ln {(1+\frac{1}{n})}^n=[1-\frac{1}{2(n+1)}+\frac{1}{2\cdot 3{(n+1)}^2}-\frac{1}{3\cdot 4{(n+1)}^3}+..]$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 140730 by liberty last updated on 12/May/21 $$\mathrm{If}\mathrm{equation}2\log (\mathrm{x}+3)=\log \mathrm{ax}$$$$\mathrm{has}\mathrm{only}\mathrm{one}\mathrm{solution}.\mathrm{find}\mathrm{the}$$$$\mathrm{value}\mathrm{of}\mathrm{a}.$$ Answered by mr W last updated on 12/May/21 $${a}\neq\mathrm{0}…

Question Number 9516 by Joel575 last updated on 12/Dec/16 $$\underset{k=1}{\sum ^n}\lfloor {\log }_{2}k\rfloor =2018$$$$\mathrm{What}\mathrm{is}\mathrm{the}\mathrm{value}\mathrm{of}n?$$ Commented by sou1618 last updated on 12/Dec/16 $$\ast{K}=\lfloor{log}_{\mathrm{2}}…

Question Number 9334 by j.masanja06@gmail.com last updated on 30/Nov/16 $$\mathrm{express}\mathrm{the}\mathrm{following}\mathrm{in}\mathrm{form}\mathrm{of}\log \mathrm{a}\left(\mathrm{f}\left(\mathrm{x}\right)\right)$$$$\left(\mathrm{i}\right){4\log }_{\mathrm{a}}\mathrm{x}-{\log }_{\mathrm{a}}({\mathrm{x}}^2+{\mathrm{x}}^3)$$$$\left(\mathrm{ii}\right){\log }_{\mathrm{a}}\mathrm{x}+{\log }_{\mathrm{a}}(\mathrm{x}+3)$$ Answered by mrW…

Question Number 74753 by necxxx last updated on 30/Nov/19 $$evaluate{5}^{\sqrt{\log 7_5}}-7^{\sqrt{\log 5_7}}$$ Commented by mr W last updated on 30/Nov/19 $${what}\:{is}\:\mathrm{log}\:\mathrm{7}_{\mathrm{5}} ?\:{the}\:{same}\:{as}\:\mathrm{log}_{\mathrm{5}}…