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Popular >

e^2x=2e^x

Solution

e^{2} x = 2 e^{x}

Solution

x = 2, x = - W_{0} (- \frac{2}{e ^{2}})

+1

Decimal Notation

x = 2, x = 0.40637 \dots

Solution steps

e^{2} x = 2 e^{x}

Prepare

e^{2} x = 2 e^{x}

for Lambert form:

e^{2 - x} x = 2

Rewrite the equation with

- x = u

and

x = - u

e^{2 - (- u)} (- u) = 2

Simplify

- e^{2 + u} u = 2

Rewrite

- e^{2 + u} u = 2

in Lambert form:

e^{u} u = - \frac{2}{e ^{2}}

Solve

e^{u} u = - \frac{2}{e ^{2}} : u = - 2, u = W_{0} (- \frac{2}{e ^{2}})

u = - 2, u = W_{0} (- \frac{2}{e ^{2}})

Substitute back

u = - x,

solve for

x

Solve

- x = - 2 : x = 2

Solve

- x = W_{0} (- \frac{2}{e ^{2}}) : x = - W_{0} (- \frac{2}{e ^{2}})

x = 2, x = - W_{0} (- \frac{2}{e ^{2}})

Popular Examples

7^{x^2+2x}=49^{-3x-5}

7^{x^{2} + 2 x} = 4 9^{- 3 x - 5}

2^{4x-1}=32^{x+1}

2^{4 x - 1} = 3 2^{x + 1}

e^{2 x} = e^{3 - x}

solvefor x,2^x+2^y=10 solve for

x, 2^{x} + 2^{y} = 10

1 1^{2 x + 5} = 1

Frequently Asked Questions (FAQ)

What is the answer to e^2x=2e^x ?
The answer to e^2x=2e^x is x=2,x=-\W_{0}(-2/(e^2))