Question Number 223512 by fantastic last updated on 27/Jul/25 $${If}\:\frac{\mathrm{log}\:{x}}{{y}−{z}}=\frac{\mathrm{log}\:{y}}{{z}−{x}}=\frac{\mathrm{log}\:{z}}{{x}−{y}} \\ $$$${prove}\:{xyz}=\mathrm{1} \\ $$ Answered by mr W last updated on 27/Jul/25 $$\frac{\mathrm{log}\:{x}}{{y}−{z}}=\frac{\mathrm{log}\:{y}}{{z}−{x}}=\frac{\mathrm{log}\:{z}}{{x}−{y}}=\frac{\mathrm{1}}{{k}}\:\:\left({k}\neq\mathrm{0}\right) \\ $$$${y}−{z}={k}\:\mathrm{log}\:{x}…
Question Number 223513 by fantastic last updated on 27/Jul/25 $${If}\:{x}=\mathrm{log}\:_{{a}} {bc}\:,\:{y}=\mathrm{log}\:_{{b}} {ca}\:,\:{z}=\mathrm{log}\:_{{c}} {ab} \\ $$$${prove}\:{that}\:{x}+{y}+{z}={xyz}−\mathrm{2} \\ $$ Answered by som(math1967) last updated on 27/Jul/25 $$\:\mathrm{1}+{x}=\mathrm{1}+{log}_{{a}}…
Question Number 223514 by fantastic last updated on 27/Jul/25 $$\mathrm{log}\:_{\mathrm{8}} \left[\mathrm{log}\:_{\mathrm{2}} \left\{\mathrm{log}\:_{\mathrm{3}} \left(\mathrm{4}^{{x}} +\mathrm{17}\right)\right\}\right]=\frac{\mathrm{1}}{\mathrm{3}} \\ $$$${x}=?? \\ $$ Answered by som(math1967) last updated on 27/Jul/25…
Question Number 222929 by gabthemathguy25 last updated on 11/Jul/25 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 222799 by fantastic last updated on 07/Jul/25 $${x}^{{x}^{{y}} } =\mathrm{9}^{{xy}} \\ $$$${x}+{y}=\mathrm{1} \\ $$ Commented by mr W last updated on 07/Jul/25 $${obvious}:\:{x}=\mathrm{1},\:{y}=\mathrm{0}…
Question Number 222697 by gabthemathguy25 last updated on 05/Jul/25 Answered by gregori last updated on 05/Jul/25 $$\:\sqrt[{\mathrm{3}}]{{e}^{\mathrm{2ln}\:\left(\mathrm{81}\right)} }\:=\:\left(\mathrm{81}^{\frac{\mathrm{2}}{\mathrm{3}}} \right)=\:\mathrm{9}^{\frac{\mathrm{4}}{\mathrm{3}}} \\ $$$$\:\sqrt[{\mathrm{4}}]{\left(\mathrm{3}^{\mathrm{log}\:_{\mathrm{9}} \left(\mathrm{9}^{\mathrm{2}} \right)} \right)^{\mathrm{2}} }\:=\:\sqrt{\mathrm{9}}=\:\mathrm{9}^{\frac{\mathrm{1}}{\mathrm{2}}}…
Question Number 222679 by fantastic last updated on 04/Jul/25 $${If}\:{x}=\underset{{x}=\mathrm{1}} {\overset{\mathrm{10}} {\prod}}{x}\:{then}\:\frac{\mathrm{1}}{\mathrm{log}\:_{\mathrm{2}} {x}}+\frac{\mathrm{1}}{\mathrm{log}\:_{\mathrm{3}} {x}}+\frac{\mathrm{1}}{\mathrm{log}\:_{\mathrm{4}} {x}}…+\frac{\mathrm{1}}{\mathrm{log}\:_{\mathrm{10}} {x}}=?? \\ $$ Answered by Tawa11 last updated on 04/Jul/25…
Question Number 222104 by efronzo1 last updated on 17/Jun/25 $$\:\:\:\:\mathrm{log}\:_{\mathrm{4}} \:\mathrm{x}\:−\:\mathrm{log}\:_{\mathrm{x}^{\mathrm{2}} } \:\mathrm{8}\:=\:\mathrm{1} \\ $$$$\:\:\:\:\mathrm{x}\:=?\: \\ $$ Answered by mr W last updated on 17/Jun/25…
Question Number 222007 by klipto last updated on 14/Jun/25 $$\boldsymbol{\mathrm{x}}\sqrt{\mathrm{1}+\boldsymbol{\mathrm{x}}^{\mathrm{2}} }+\boldsymbol{\mathrm{log}}\left(\boldsymbol{\mathrm{x}}+\sqrt{\mathrm{1}+\boldsymbol{\mathrm{x}}^{\mathrm{2}} }\right)=\mathrm{12}.\mathrm{5} \\ $$$$\mathrm{find}\:\boldsymbol{\mathrm{x}}^{\mathrm{2}} \:\left(\mathrm{answer}\:\mathrm{should}\:\mathrm{not}\:\mathrm{be}\:\mathrm{in}\:\mathrm{decimal}\right) \\ $$ Commented by AntonCWX8 last updated on 15/Jun/25 $${Do}\:{you}\:{mean}\:{to}\:{find}\:{a}\:{close}\:{form}?…
Question Number 221896 by fantastic last updated on 12/Jun/25 $${If}\:\mathrm{log}\underset{\mathrm{10}} {\:}\mathrm{7}={a}\:,{then}\:\mathrm{log}\underset{\mathrm{10}} {\:}\left(\frac{\mathrm{1}}{\mathrm{70}}\right)=? \\ $$ Answered by fantastic last updated on 12/Jun/25 $$\mathrm{log}\underset{\mathrm{10}} {\:}\mathrm{7}={a} \\ $$$$\:{so}\:\mathrm{10}^{{a}}…