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Category: Logarithms

Question-200224

Question Number 200224 by cortano12 last updated on 15/Nov/23 Answered by Rasheed.Sindhi last updated on 16/Nov/23 $$\begin{cases}{{yx}^{\mathrm{log}_{{y}} {x}\:} ={x}^{\frac{\mathrm{5}}{\mathrm{2}}} ……………\left({i}\right)}\\{\mathrm{log}_{\mathrm{4}} {y}.\mathrm{log}_{{y}} \left({y}−\mathrm{3}{x}\right)=\mathrm{1}…\left({ii}\right)\:\:}\end{cases} \\ $$$$\left({ii}\right)\Rightarrow\:\frac{\mathrm{1}}{\mathrm{log}_{{y}} \mathrm{4}\:}=\frac{\mathrm{1}}{\mathrm{log}_{{y}}…

Question-199956

Question Number 199956 by cortano12 last updated on 11/Nov/23 Answered by Frix last updated on 11/Nov/23 $$\left(\mathrm{1}\right)\:\Rightarrow\:{x}={y}\left({y}^{\mathrm{2}} +{y}+\mathrm{2}\right)\wedge{y}>\mathrm{0} \\ $$$$\left(\mathrm{2}\right)\:\Rightarrow\:\frac{{x}}{{y}}=\mathrm{4}\vee\frac{{x}}{{y}}=\mathrm{8} \\ $$$$\Rightarrow \\ $$$${x}=\mathrm{4}\wedge{y}=\mathrm{1}\:\vee\:{x}=\mathrm{16}\wedge{y}=\mathrm{2} \\…

solve-for-x-log100-log-2-x-10-

Question Number 198124 by stevoh last updated on 10/Oct/23 $${solve}\:{for}\:{x}\:{log}\mathrm{100}+{log}\left(\mathrm{2}+{x}\right)=\mathrm{10} \\ $$ Answered by a.lgnaoui last updated on 10/Oct/23 $$\:\boldsymbol{\mathrm{xlog}}\mathrm{100}+\boldsymbol{\mathrm{log}}\left(\mathrm{2}+\boldsymbol{\mathrm{x}}\right)=\mathrm{10} \\ $$$$ \\ $$$$\:\:\:\:\mathrm{x}=\mathrm{10}−\mathrm{log}\left(\mathrm{2}+\mathrm{x}\right)\:\:\:\:\:\mathrm{log100}=\mathrm{2} \\…

pi-2-0-ln-cost-sint-dt-

Question Number 197099 by Erico last updated on 07/Sep/23 $$\underset{\:\mathrm{0}} {\int}^{\:\frac{\pi}{\mathrm{2}}} \frac{\mathrm{ln}\left(\mathrm{cos}{t}\right)}{\mathrm{sin}{t}}\:\mathrm{d}{t}=??? \\ $$ Answered by witcher3 last updated on 07/Sep/23 $$=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{sin}\left(\mathrm{t}\right)\mathrm{ln}\left(\mathrm{cos}\left(\mathrm{t}\right)\right)}{\mathrm{1}−\mathrm{cos}^{\mathrm{2}} \left(\mathrm{t}\right)}\mathrm{dt},\mathrm{cos}\left(\mathrm{t}\right)=\mathrm{y}…

If-ax-loga-bx-logb-then-prove-that-x-1-ab-

Question Number 196690 by MATHEMATICSAM last updated on 29/Aug/23 $$\mathrm{If}\:\left({ax}\right)^{\mathrm{log}{a}} \:=\:\left({bx}\right)^{\mathrm{log}{b}} \:\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$${x}\:=\:\frac{\mathrm{1}}{{ab}}\:. \\ $$ Answered by BaliramKumar last updated on 29/Aug/23 $$\mathrm{loga}\centerdot\mathrm{log}\left(\mathrm{ax}\right)\:=\:\mathrm{logb}\centerdot\mathrm{log}\left(\mathrm{bx}\right) \\…