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 $$\frac{\mathrm{log}\:{x}}{{y}−{z}}=\frac{\mathrm{log}\:{y}}{{z}−{x}}=\frac{\mathrm{log}\:{z}}{{x}−{y}}=\frac{\mathrm{1}}{{k}}\:\:\left({k}\neq\mathrm{0}\right) \\ $$$${y}−{z}={k}\:\mathrm{log}\:{x}…
Question Number 223529 by Ismoiljon_008 last updated on 27/Jul/25 Answered by mr W last updated on 27/Jul/25 Commented by mr W last updated on 27/Jul/25…
Question Number 223513 by fantastic last updated on 27/Jul/25 $${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…
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Question Number 223525 by Nicholas666 last updated on 27/Jul/25 $$ \\ $$$$\:\:\:\:{I}\:=\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \int_{\mathrm{0}} ^{\mathrm{2}\pi} \int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\mid\:\mathrm{cos}\:{x}\:+\:\mathrm{cos}\:{y}\:+\:\mathrm{cos}\:{z}\:\:\mid\:\:{dxdydz}\:\:\:\:\:\:\:\: \\ $$$$ \\ $$ Terms of Service…
Question Number 223523 by Nicholas666 last updated on 27/Jul/25 Commented by Nicholas666 last updated on 27/Jul/25 $$\:\:\boldsymbol{\mathrm{how}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{this}}\:\boldsymbol{\mathrm{problem}}\:?\: \\ $$$$ \\ $$ Terms of Service Privacy…
Question Number 223487 by Tawa11 last updated on 26/Jul/25 Let Φ be the hyperbola xy = b², b ≠ 0, and P be a point…
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