Question

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

Answer 1

$\dfrac{e^x-e^{-x}}{e^x+e^{-x}}=t\\\\ \dfrac{e^{2x}-1}{e^{2x}+1}=t\\\\ e^{2x}-1=t(e^{2x}+1)\\\\ e^{2x}-1=e^{2x}t+t\\\\ e^{2x}-e^{2x}t=t+1\\\\ e^{2x}(1-t)=t+1\\\\ e^{2x}=\dfrac{t+1}{1-t}\\\\ e^{2x}=-\dfrac{t+1}{t-1}\\\\ 2x=\ln\left(-\dfrac{t+1}{t-1}\right)\\\\ x=\dfrac{\ln\left(-\dfrac{t+1}{t-1}\right)}{2}\qquad t\in(-1,1)$

Answer 2

Answer:

d on edge

Step-by-step explanation: