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Popular >

solvefor x,t(x)=e^x

Solution

solve for

x, t (x) = e^{x}

Solution

x = - W (- \frac{1}{t})

Solution steps

t (x) = e^{x}

Prepare

t (x) = e^{x}

for Lambert form:

t x e^{- x} = 1

Rewrite the equation with

- x = u

and

x = - u

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

Rewrite

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

in Lambert form:

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

Solve

e^{u} u = - \frac{1}{t} : u = W (- \frac{1}{t})

u = W (- \frac{1}{t})

Substitute back

u = - x,

solve for

x

Solve

- x = W (- \frac{1}{t}) : x = - W (- \frac{1}{t})

x = - W (- \frac{1}{t})

Popular Examples

2 5^{x} - 3 \cdot 5^{x} = 0

3^{2 x - 7} = 81

8^{- x} = 1.2

e^{3 k} = 27

16*4^{x-4}=9^{2x-3}

16 \cdot 4^{x - 4} = 9^{2 x - 3}

Frequently Asked Questions (FAQ)

What is the answer to solvefor x,t(x)=e^x ?
The answer to solvefor x,t(x)=e^x is x=-\W(-1/t)