Question

\((1+e^{2y})\)=x,express y in terms of x.

Answer/Explanation

State  \(1+e^{2y}=e^{x}\)

Make y the subject 

Obtain answer \(y=\frac{1}{2}(e^{x}-1)\)

Question

Showing all necessary working, solve the equation \(\frac{2e^{x}+e^{-x}}{e^{x}-e^{-x}}\)= 4, giving your answer correct to
2 decimal places.

Answer/Explanation

Rearrange the equation in the form\( ae^{2x}=b or ae^{x}=be^{-x}\)

Obtain correct equation in either form with a = 2 and b = 5

Use correct method to solve for x

Obtain answer x = 0.46