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Popular >

1+x=e^x

Solution

1 + x = e^{x}

Solution

x = 0

Solution steps

1 + x = e^{x}

Prepare

1 + x = e^{x}

for Lambert form:

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

Rewrite the equation with

- x - 1 = u

and

x = - u - 1

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

Simplify

- e^{u + 1} u = 1

Rewrite

- e^{u + 1} u = 1

in Lambert form:

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

Solve

e^{u} u = - \frac{1}{e} : u = - 1

u = - 1

Substitute back

u = - x - 1,

solve for

x

Solve

- x - 1 = - 1 : x = 0

x = 0

Popular Examples

- e^{2 x} + 3 x + 4 = 0

(((2/3)^n)/4)/(9)=(2/3)^4

\frac{\frac{( \frac{2}{3} ) ^{n}}{4}}{9} = (\frac{2}{3})^{4}

((3^{2x+3}))/((9^3))=9^{14}

\frac{( 3 ^{2 x + 3} )}{( 9 ^{3} )} = 9^{14}

solvefor b,4^{log_{2}(a^2b)}=3a^3 solve for

b, 4^{l o g_{2} (a^{2} b)} = 3 a^{3}

3^x-1+3^x-2+3^x-3=13

3^{x} - 1 + 3^{x} - 2 + 3^{x} - 3 = 13

Frequently Asked Questions (FAQ)

What is the answer to 1+x=e^x ?
The answer to 1+x=e^x is x=0