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Popular >

e^x=-9x

Solution

e^{x} = - 9 x

Solution

x = - W_{0} (\frac{1}{9})

+1

Decimal Notation

x = - 0.10048 \dots

Solution steps

e^{x} = - 9 x

Prepare

e^{x} = - 9 x

for Lambert form:

1 = - 9 e^{- x} x

Rewrite the equation with

- x = u

and

x = - u

1 = - 9 e^{u} (- u)

Rewrite

1 = - 9 e^{u} (- u)

in Lambert form:

e^{u} u = \frac{1}{9}

Solve

e^{u} u = \frac{1}{9} : u = W_{0} (\frac{1}{9})

u = W_{0} (\frac{1}{9})

Substitute back

u = - x,

solve for

x

Solve

- x = W_{0} (\frac{1}{9}) : x = - W_{0} (\frac{1}{9})

x = - W_{0} (\frac{1}{9})

Popular Examples

27^x-3^{x+2}=9^x-9

2 7^{x} - 3^{x + 2} = 9^{x} - 9

10^{x+2}-10^x=9900

1 0^{x + 2} - 1 0^{x} = 9900

2e^{2x}+2e^{-2x}-e^x+e^{-x}=7

2 e^{2 x} + 2 e^{- 2 x} - e^{x} + e^{- x} = 7

10^{x+8}=6^{2x}

1 0^{x + 8} = 6^{2 x}

34.416e^{-0.18t}=6

34.416 e^{- 0.18 t} = 6

Frequently Asked Questions (FAQ)

What is the answer to e^x=-9x ?
The answer to e^x=-9x is x=-\W_{0}(1/9)