Question

Solve for x. (e^x-e^-x)/((e^x+e^-x)=t

Answer 1

`(e^x-e^(-x))/(e^x+e^(-x))=t\\\\ (e^(2x)-1)/(e^(2x)+1)=t\\\\ e^(2x)-1=t(e^(2x)+1)\\\\ e^(2x)-1=e^(2x)t+t\\\\ e^(2x)-e^(2x)t=t+1\\\\ e^(2x)(1-t)=t+1\\\\ e^(2x)=(t+1)/(1-t)\\\\ e^(2x)=-(t+1)/(t-1)\\\\ 2x=\ln\left(-(t+1)/(t-1)\right)\\\\ x=(\ln\left(-(t+1)/(t-1)\right))/(2)\qquad t\in(-1,1)`

Answer 2

d on edge

Explanation: