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Popular >

e^x-4+x=0

Solution

e^{x} - 4 + x = 0

Solution

x = - W_{0} (e^{4}) + 4

+1

Decimal Notation

x = 1.07372 \dots

Solution steps

e^{x} - 4 + x = 0

Prepare

e^{x} - 4 + x = 0

for Lambert form:

1 = (- x + 4) e^{- x}

Rewrite the equation with

- x + 4 = u

and

x = - u + 4

1 = (- (- u + 4) + 4) e^{- (- u + 4)}

Simplify

1 = e^{u - 4} u

Rewrite

1 = e^{u - 4} u

in Lambert form:

e^{u} u = e^{4}

Solve

e^{u} u = e^{4} : u = W_{0} (e^{4})

u = W_{0} (e^{4})

Substitute back

u = - x + 4,

solve for

x

Solve

- x + 4 = W_{0} (e^{4}) : x = - W_{0} (e^{4}) + 4

x = - W_{0} (e^{4}) + 4

Popular Examples

8^x+2^{3x+1}-8^{x+2}=-488

8^{x} + 2^{3 x + 1} - 8^{x + 2} = - 488

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

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

solvefor y,2^y-1=x solve for

y, 2^{y} - 1 = x

5 + e^{2 x + 1} = 8

4 e^{7 x} = 17

Frequently Asked Questions (FAQ)

What is the answer to e^x-4+x=0 ?
The answer to e^x-4+x=0 is x=-\W_{0}(e^4)+4