# Category: Logarithms

## 0-1-x-ln-x-dx-

Question Number 208083 by nachosam last updated on 04/Jun/24 $$\int_{\left[\mathrm{0},\infty\right]} \left(\frac{\mathrm{1}}{{x}}\right)^{{ln}\left({x}\right)} {dx} \\$$$$\\$$ Answered by Saiki last updated on 04/Jun/24 Answered by…

## x-2-log-3-x-2-2x-2-3-log-9-2x-3-3log-3-x-2x-3-

Question Number 204300 by depressiveshrek last updated on 11/Feb/24 $${x}^{\mathrm{2}} \mathrm{log}_{\mathrm{3}} {x}^{\mathrm{2}} −\left(\mathrm{2}{x}^{\mathrm{2}} +\mathrm{3}\right)\mathrm{log}_{\mathrm{9}} \left(\mathrm{2}{x}+\mathrm{3}\right)=\mathrm{3log}_{\mathrm{3}} \left(\frac{{x}}{\mathrm{2}{x}+\mathrm{3}}\right) \\$$ Answered by Rasheed.Sindhi last updated on 11/Feb/24…

## Question-204174

Question Number 204174 by patrice last updated on 08/Feb/24 Answered by Faetmaaa last updated on 27/Feb/24 $$\left.\mathrm{3}\right)- \\$$$$\forall{n}\in\boldsymbol{\mathrm{N}}^{\bigstar} \\$${S}_{{n}} \:=\:\frac{\mathrm{1}}{{n}}\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\mathrm{ln}\left(\frac{{k}}{{n}}\right) \\…