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Popular >

t=e^{λ(t-1)}

Solution

t = e^{λ (t - 1)}

Solution

t = - \frac{W ( - \frac{λ}{e ^{λ}} )}{λ}

Solution steps

t = e^{λ (t - 1)}

Prepare

t = e^{λ (t - 1)}

for Lambert form:

t e^{- λ (t - 1)} = 1

Rewrite the equation with

- λ t = u

and

t = - \frac{u}{λ}

(- \frac{u}{λ}) e^{- λ ((- \frac{u}{λ}) - 1)} = 1

Simplify

- \frac{e ^{u + λ} u}{λ} = 1

Rewrite

- \frac{e ^{u + λ} u}{λ} = 1

in Lambert form:

e^{u} u = - \frac{λ}{e ^{λ}}

Solve

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

u = W (- \frac{λ}{e ^{λ}})

Substitute back

u = - λ t,

solve for

t

Solve

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

t = - \frac{W ( - \frac{λ}{e ^{λ}} )}{λ}

Popular Examples

solvefor c,1=e^{e(0)+c}solve for

c, 1 = e^{e (0) + c}

2e^x=5sqrt(e^x)+12

2 e^{x} = 5 e^{x} + 12

solvefor t,5^t=7 solve for

t, 5^{t} = 7

125^{3x-4}=25^{4x+2}

12 5^{3 x - 4} = 2 5^{4 x + 2}

- 1 = e^{x}

Frequently Asked Questions (FAQ)

What is the answer to t=e^{λ(t-1)} ?
The answer to t=e^{λ(t-1)} is t=-(\W(-λ/(e^λ)))/λ