Shanya asked in Science & MathematicsMathematics · 2 months ago

# e^2x-4e^x+3=0 help please correct me if I'm wrong?

"x - In(3)" is my answer and says that the answer should be in decimal form so it should be "1.09"? and says that round off the answer to 1 decimal place so it could be "1.1"?

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• 2 months ago

e^(2x) - 4e^x + 3 = 0

Let u = e^x, so we have:

u^2 - 4u + 3 = 0

u^2 - u - 3u + 3 = 0

u(u - 1) - 3(u - 1) = 0

(u - 3)(u - 1) = 0

u = 3 or u = 1

e^x = 3 or e^x = 1

x = ln(3) + 2*i*pi*n, for any integer n, or

x = ln(1) + 2*i*pi*n = 2*i*pi*n, for any integer n

x =~ 1.098612 + 6.283185in, for any integer n, or

x =~ 6.283185in, for any integer n

x = ln(3) or x = 0

x =~ 1.098612 or x = 0

• 2 months ago

e²ˣ - 4eˣ + 3 = 0

(eˣ)² - 4eˣ + 3 = 0

(eˣ - 1)(eˣ - 3) = 0

eˣ = 1 or eˣ = 3

x = ln(1)  or  x = ln(3)

x = 0.0  or  x = 1.1

x has two roots: 0.0 and 1.1

• 2 months ago

e^(2x) - 4e^(x) + 3 = 0

(e^(x) - 1)(e^(x) - 3) = 0

e^(x) - 1 = 0, e^(x) - 3 = 0

e^(x) = 1, e^(x) = 3

x = ln(1), x = ln(3)

x = 0, x = 1.098 or 1.1