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Popular >

e^{2x}x=2

Solution

e^{2 x} x = 2

Solution

x = \frac{W _{0} ( 4 )}{2}

+1

Decimal Notation

x = 0.60108 \dots

Solution steps

e^{2 x} x = 2

Rewrite the equation with

2 x = u

and

x = \frac{u}{2}

e^{u} (\frac{u}{2}) = 2

Rewrite

e^{u} (\frac{u}{2}) = 2

in Lambert form:

e^{u} u = 4

Solve

e^{u} u = 4 : u = W_{0} (4)

u = W_{0} (4)

Substitute back

u = 2 x,

solve for

x

Solve

2 x = W_{0} (4) : x = \frac{W _{0} ( 4 )}{2}

x = \frac{W _{0} ( 4 )}{2}

Popular Examples

4^x-8\times 2^x=2^{x-2}-2

4^{x} - 8 \times 2^{x} = 2^{x - 2} - 2

5^{3x+2}=25^{x-8}

5^{3 x + 2} = 2 5^{x - 8}

2 7^{2 x - 3} = 27

5^{- x} = 15

2\times 3^{1-x}+3^{x-1}=3^x

2 \times 3^{1 - x} + 3^{x - 1} = 3^{x}

Frequently Asked Questions (FAQ)

What is the answer to e^{2x}x=2 ?
The answer to e^{2x}x=2 is x=(\W_{0}(4))/2