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Popular >

e^{2x}-6e^x+8=0

Solution

e^{2 x} - 6 e^{x} + 8 = 0

Solution

x = 2 ln (2), x = ln (2)

+1

Decimal Notation

x = 1.38629 \dots, x = 0.69314 \dots

Solution steps

e^{2 x} - 6 e^{x} + 8 = 0

Apply exponent rules

(e^{x})^{2} - 6 e^{x} + 8 = 0

Rewrite the equation with

e^{x} = u

(u)^{2} - 6 u + 8 = 0

Solve

u^{2} - 6 u + 8 = 0 : u = 4, u = 2

u = 4, u = 2

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = 4 : x = 2 ln (2)

Solve

e^{x} = 2 : x = ln (2)

x = 2 ln (2), x = ln (2)

Popular Examples

x^2e^{2x}+2xe^{2x}=8e^{2x}

x^{2} e^{2 x} + 2 x e^{2 x} = 8 e^{2 x}

4^{2x+6}=64^{2x-4}

4^{2 x + 6} = 6 4^{2 x - 4}

5^{x} = 16

e^x+15e^{-x}-8=0

e^{x} + 15 e^{- x} - 8 = 0

3^{x-9}=81^{5x+1}

3^{x - 9} = 8 1^{5 x + 1}

Frequently Asked Questions (FAQ)

What is the answer to e^{2x}-6e^x+8=0 ?
The answer to e^{2x}-6e^x+8=0 is x=2ln(2),x=ln(2)