$\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)



$

8 0

3 years ago

Read 2 more answers

How do you turn -8/9 into a decimal and percent?

monitta

You need to divide the numerator by the denominator so it should be 8 divided by 9 to turn it into a percent multiply the decimal you get by 100. Hope this helps!

8 0

3 years ago

Read 2 more answers