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Author: Tinku Tara

0-1-ln-x-x-ln-3-1-x-1-x-dx-

Question Number 223534 by Tawa11 last updated on 28/Jul/25 $$\int_{\:\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{ln}\left(\mathrm{x}\right)}{\mathrm{x}}\:\mathrm{ln}^{\mathrm{3}} \left(\frac{\mathrm{1}\:\:−\:\:\mathrm{x}}{\mathrm{1}\:\:+\:\:\mathrm{x}}\right)\:\mathrm{dx} \\ $$ Answered by MathematicalUser2357 last updated on 31/Jul/25 $$\:\cancel{\:} \\ $$…

x-y-36-xy-max-

Question Number 223538 by fantastic last updated on 28/Jul/25 $${x}+{y}=\mathrm{36} \\ $$$${xy}_{{max}} =?? \\ $$ Answered by Frix last updated on 28/Jul/25 $$\mathrm{Max}\:\mathrm{at}\:{x}={y}=\mathrm{18}\:\mathrm{because}\:\mathrm{out}\:\mathrm{of}\:\mathrm{all}\:\mathrm{rectangles} \\ $$$$\mathrm{with}\:\mathrm{given}\:\mathrm{circumference}\:\mathrm{the}\:\mathrm{square}\:\mathrm{has}\:\mathrm{the}…

If-log-x-y-z-log-y-z-x-log-z-x-y-prove-xyz-1-

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}…