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Popular >

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

Solution

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

Solution

x = ln (2)

+1

Decimal Notation

x = 0.69314 \dots

Solution steps

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

Apply exponent rules

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

Rewrite the equation with

e^{x} = u

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

Solve

u^{2} - 4 u + 4 = 0 : u = 2

u = 2

Substitute back

u = e^{x},

solve for

x

Solve

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

x = ln (2)

Popular Examples

2^{x} + 4 x + 12 = 0

5e^{2-x}=10^{x+4}

5 e^{2 - x} = 1 0^{x + 4}

-(16x-16)e^{-x}=0

- (16 x - 16) e^{- x} = 0

2^{x+1}+6(2^{x-1})=12

2^{x + 1} + 6 (2^{x - 1}) = 12

\frac{1}{36} = 6^{x - 3}

Frequently Asked Questions (FAQ)

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