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Popular >

5=4+x+e^x

Solution

5 = 4 + x + e^{x}

Solution

x = 0

Solution steps

5 = 4 + x + e^{x}

Prepare

5 = 4 + x + e^{x}

for Lambert form:

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

Rewrite the equation with

- x + 1 = u

and

x = - u + 1

1 = (- (- u + 1) + 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

8^{2x}=128^{x-1}

8^{2 x} = 12 8^{x - 1}

5^{x - 1} = 125

e^{x} + 2 x = 0

1.2 x = 1. 2^{x}

16^x+3*4^x-10=0

1 6^{x} + 3 \cdot 4^{x} - 10 = 0

Frequently Asked Questions (FAQ)

What is the answer to 5=4+x+e^x ?
The answer to 5=4+x+e^x is x=0