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Popular >

e^{2x}-4e^x+3=0

Solution

e^{2 x} - 4 e^{x} + 3 = 0

Solution

x = ln (3), x = 0

+1

Decimal Notation

x = 1.09861 \dots, x = 0

Solution steps

e^{2 x} - 4 e^{x} + 3 = 0

Apply exponent rules

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

Rewrite the equation with

e^{x} = u

(u)^{2} - 4 u + 3 = 0

Solve

u^{2} - 4 u + 3 = 0 : u = 3, u = 1

u = 3, u = 1

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = 3 : x = ln (3)

Solve

e^{x} = 1 : x = 0

x = ln (3), x = 0

Popular Examples

8^{x} = 4

e^{x} = 6

1 0^{3 - x} = 1

e^{- 2 x} = 0

2^{x+1}=5^{1-2x}

2^{x + 1} = 5^{1 - 2 x}

Frequently Asked Questions (FAQ)

What is the answer to e^{2x}-4e^x+3=0 ?
The answer to e^{2x}-4e^x+3=0 is x=ln(3),x=0