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Popular >

4=3+x+e^x

Solution

4 = 3 + x + e^{x}

Solution

x = 0

Solution steps

4 = 3 + x + e^{x}

Prepare

4 = 3 + 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

86400=50000(1+0.2)^x

86400 = 50000 (1 + 0.2)^{x}

solvefor t,x=e^{2t}solve for

t, x = e^{2 t}

125^{x-3}=25^{2x+1}

12 5^{x - 3} = 2 5^{2 x + 1}

0^{x} = 0

e^{3 t} = 100

Frequently Asked Questions (FAQ)

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