Question Number 227232 by fantastic2 last updated on 07/Jan/26 $$\left(\mathrm{64}−\left(\mathrm{8}\pi+\mathrm{4}\pi\right)\right)−\left(\mathrm{8}\pi−\left(\mathrm{4}\left(\mathrm{tan}^{−\mathrm{1}} \mathrm{2}+\mathrm{4tan}^{−\mathrm{1}} \frac{\mathrm{1}}{\mathrm{2}}−\mathrm{2}\right)+\mathrm{8}\left(\pi−\mathrm{2}\right)\right)\right)−\left(\mathrm{64}−\left(\mathrm{16}\pi+\mathrm{8}\pi−\mathrm{16}\left(\mathrm{tan}^{−\mathrm{1}} \mathrm{2}+\mathrm{4tan}^{−\mathrm{1}} \frac{\mathrm{1}}{\mathrm{2}}−\mathrm{2}\right)\right)\right)−\left(\mathrm{3}.\mathrm{2}+\mathrm{2}+\left(\mathrm{32tan}^{−\mathrm{1}} \frac{\mathrm{4}.\mathrm{8}}{\mathrm{6}.\mathrm{4}}−\mathrm{32sin}\:\mathrm{tan}^{−\mathrm{1}} \frac{\mathrm{4}.\mathrm{8}}{\mathrm{6}.\mathrm{4}}\right)−\pi\right)+\mathrm{4}\left(\mathrm{tan}^{−\mathrm{1}} \mathrm{2}+\mathrm{4tan}^{−\mathrm{1}} \frac{\mathrm{1}}{\mathrm{2}}−\mathrm{2}\right) \\ $$ Terms of Service Privacy Policy…
Question Number 227192 by gregori last updated on 05/Jan/26 $$\:\:\:\:{x}^{\mathrm{log}\:\mathrm{2}{x}} \:=\:\mathrm{5}\:\Rightarrow{x}=\:? \\ $$ Answered by Kassista last updated on 05/Jan/26 $$ \\ $$$${ln}\left({x}^{{ln}\left(\mathrm{2}{x}\right)} \right)={ln}\left(\mathrm{5}\right) \\…
Question Number 223512 by fantastic last updated on 27/Jul/25 $${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…