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Popular >

1=x+e^x

Solution

1 = x + e^{x}

Solution

x = 0

Solution steps

1 = x + e^{x}

Prepare

1 = x + e^{x}

for Lambert form:

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

Rewrite the equation with

- x + 1 = u

and

x = - u + 1

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

409 6^{x} = 8

2^x*2^{3x-8}=16

2^{x} \cdot 2^{3 x - 8} = 16

16^x-5*2^{2x-1}+1=0

1 6^{x} - 5 \cdot 2^{2 x - 1} + 1 = 0

e^{x} + 1 = 4

6 4^{x} = 8

Frequently Asked Questions (FAQ)

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