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Popular >

e^x+x-1=0

Solution

e^{x} + x - 1 = 0

Solution

x = 0

Solution steps

e^{x} + x - 1 = 0

Prepare

e^{x} + x - 1 = 0

for Lambert form:

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

Rewrite the equation with

- x + 1 = u

and

x = - u + 1

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

Simplify

1 = e^{u - 1} u

Rewrite

1 = e^{u - 1} u

in Lambert form:

e^{u} u = e

Solve

e^{u} u = e : u = 1

u = 1

Substitute back

u = - x + 1,

solve for

x

Solve

- x + 1 = 1 : x = 0

x = 0

Popular Examples

5^{6x}-6(125^x)+5=0

5^{6 x} - 6 (12 5^{x}) + 5 = 0

4 \cdot 2^{x} = 2^{6 x + 3}

9^{2-x}=(1/3)^{2x+1}

9^{2 - x} = (\frac{1}{3})^{2 x + 1}

(\frac{1}{4})^{x} = 4

(sqrt(2))^k=0.25

(2)^{k} = 0.25

Frequently Asked Questions (FAQ)

What is the answer to e^x+x-1=0 ?
The answer to e^x+x-1=0 is x=0