Question and Answers Forum

All Questions      Topic List

Others Questions

Previous in All Question      Next in All Question      

Previous in Others      Next in Others      

Question Number 68676 by Rio Michael last updated on 14/Sep/19

Solve the equation  tanh^(−1) (((x−2)/(x+1))) = ln 2  show that the set {1,2,4,8}  under ×_(15)  ,multiplication mod 15  forms a group.

$${Solve}\:{the}\:{equation} \\ $$$${tanh}^{−\mathrm{1}} \left(\frac{{x}−\mathrm{2}}{{x}+\mathrm{1}}\right)\:=\:{ln}\:\mathrm{2} \\ $$$${show}\:{that}\:{the}\:{set}\:\left\{\mathrm{1},\mathrm{2},\mathrm{4},\mathrm{8}\right\}\:\:{under}\:×_{\mathrm{15}} \:,{multiplication}\:{mod}\:\mathrm{15}\:\:{forms}\:{a}\:{group}. \\ $$

Commented by MJS last updated on 14/Sep/19

tanh^(−1)  t =((ln (1+t))/2)−((ln (1−t))/2)  e^(tanh^(−1)  t) =(√((1+t)/(1−t)))  t=((x−2)/(x+1))  ⇒  (√((2x−1)/3))=2  ⇒ x=((13)/2)

$$\mathrm{tanh}^{−\mathrm{1}} \:{t}\:=\frac{\mathrm{ln}\:\left(\mathrm{1}+{t}\right)}{\mathrm{2}}−\frac{\mathrm{ln}\:\left(\mathrm{1}−{t}\right)}{\mathrm{2}} \\ $$$$\mathrm{e}^{\mathrm{tanh}^{−\mathrm{1}} \:{t}} =\sqrt{\frac{\mathrm{1}+{t}}{\mathrm{1}−{t}}} \\ $$$${t}=\frac{{x}−\mathrm{2}}{{x}+\mathrm{1}} \\ $$$$\Rightarrow \\ $$$$\sqrt{\frac{\mathrm{2}{x}−\mathrm{1}}{\mathrm{3}}}=\mathrm{2} \\ $$$$\Rightarrow\:{x}=\frac{\mathrm{13}}{\mathrm{2}} \\ $$

Commented by Rio Michael last updated on 15/Sep/19

thank you sir

$${thank}\:{you}\:{sir} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com