Solve the equation, Check for extraneous solutions: 2e^x - 1 = 9

2eˣ-1 = 9

add 1 from both sides
2eˣ= 10

divide both sides by 2
eˣ=5

take the natural log of both sides
x = ln(5)

ln(5) = 1.60943791
x = 1.60943791