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Popular >

e^x-2+x=0

Solution

e^{x} - 2 + x = 0

Solution

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

+1

Solution steps

e^{x} - 2 + x = 0

Prepare

e^{x} - 2 + x = 0

for Lambert form:

1 = (- x + 2) e^{- x}

Rewrite the equation with

- x + 2 = u

and

x = - u + 2

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

Simplify

1 = e^{u - 2} u

Rewrite

1 = e^{u - 2} u

in Lambert form:

e^{u} u = e^{2}

Solve

e^{u} u = e^{2} : u = W_{0} (e^{2})

u = W_{0} (e^{2})

Substitute back

u = - x + 2,

solve for

x

Solve

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

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

Popular Examples

4^{x-4}+4^{x-3}+4^{x-1}=276

4^{x - 4} + 4^{x - 3} + 4^{x - 1} = 276

5^{3x}=25^{(x-1)}

5^{3 x} = 2 5^{(x - 1)}

3^x*5^{x+1}=125

3^{x} \cdot 5^{x + 1} = 125

9^{(4x-5)}=25^{(6x+2)}

9^{(4 x - 5)} = 2 5^{(6 x + 2)}

e^{3 x} = \frac{1}{64}

Frequently Asked Questions (FAQ)

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