Solve the equation

Question

e^2x − 3e^x + 2 = 0

Answer 1

e^2x − 3e^x + 2 = 0

(e^x)² − 3e^x + 2 = 0

 

Let u = e^x

 

u² - 3u + 2 = 0

(u-2)(u-1) = 0

 

u = 2 and u = 1

 

u = e^x = 2

ln(e^x) = ln(2)

x = ln(2)

u = e^x = 1
ln(e^x) = ln(1)
x = ln(1) = 0

 

The answers are x = 0 and ln(2)