Category: Logarithms

Question Number 164806 by saboorhalimi last updated on 22/Jan/22 Commented by cortano1 last updated on 22/Jan/22 $$\log {}_{12}\left(3\right)=a\Rightarrow \log {}_3\left(12\right)=\frac{1}{a}$$$$\Rightarrow 1+2\log {}_3\left(2\right)=\frac{1}{a}$$$$\Rightarrow\mathrm{log}\:_{\mathrm{3}} \left(\mathrm{2}\right)=\:\frac{\mathrm{1}−{a}}{\mathrm{2}{a}}\:…

Question Number 32885 by scientist last updated on 05/Apr/18 Answered by MJS last updated on 05/Apr/18 $$\log u=a$$$$\log v=b$$$$\log s=c$$$$\log t=d$$$$\mathrm{all}\:\mathrm{we}\:\mathrm{need}\:\mathrm{is}\:\mathrm{log}\:\frac{{p}}{{q}}=\mathrm{log}\:{p}−\mathrm{log}\:{q}…

Question Number 163061 by tounghoungko last updated on 03/Jan/22 $$\sqrt[\log {}_x\left(\frac{243}{x}\right)]{2}=\sqrt[3]{\log {}_x\left(\frac{x^5}{9}\right)}$$ Answered by mahdipoor last updated on 03/Jan/22 $${get}\:\mathrm{5}−\mathrm{2}{log}_{{x}} \mathrm{3}={u} \…

Question Number 97412 by mr W last updated on 07/Jun/20 $$prove$$$$\sqrt{2}<{\log }_{2}3<\sqrt{3}$$ Answered by bobhans last updated on 08/Jun/20 $$\sqrt{\mathrm{8}}\:<\:\sqrt{\mathrm{9}}\:\Rightarrow\mathrm{log}\:_{\mathrm{2}} \left(\sqrt{\mathrm{8}}\right)\:<\:\mathrm{log}\:_{\mathrm{2}}…

Question Number 97173 by 675480065 last updated on 06/Jun/20 Answered by Sourav mridha last updated on 06/Jun/20 $$\mathit{I}=\frac{2}{\mathit{\pi }}{\int }_{-\frac{\pi }{4}}^{\frac{+\pi }{4}}\frac{\mathit{d}\mathit{x}}{(1+{\mathit{e}}^{\mathit{s}\mathit{i}\mathit{n}\mathit{x}})(2-\mathit{c}\mathit{o}\mathit{s}2\mathit{x})}\dots \left(\mathit{i}\right)$$$$\boldsymbol{{and}}\:\boldsymbol{{also}}\:\boldsymbol{{I}}=\frac{\mathrm{2}}{\boldsymbol{\pi}}\int_{+\frac{\pi}{\mathrm{4}}} ^{−\frac{\boldsymbol{\pi}}{\mathrm{4}}} \frac{\mathrm{d}\left(−\mathrm{x}\right)}{\left(\mathrm{1}+\boldsymbol{{e}}^{\boldsymbol{{sin}}\left(−\boldsymbol{{x}}\right)}…