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Popular >

3+x+e^x=4

Solution

3 + x + e^{x} = 4

Solution

x = 0

Solution steps

3 + x + e^{x} = 4

Prepare

3 + x + e^{x} = 4

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

2^{x} = 4^{x - 1}

e^{2 x} + e^{x} = 1

10 e^{- 0.03 t} = 4

123456789=3.5(0.9825)^x

123456789 = 3.5 (0.9825)^{x}

solvefor y,(5^{-1})^3=x^y solve for

y, (5^{- 1})^{3} = x^{y}

Frequently Asked Questions (FAQ)

What is the answer to 3+x+e^x=4 ?
The answer to 3+x+e^x=4 is x=0