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Popular >

(x+2)e^{x-1}-1=0

Solution

(x + 2) e^{x - 1} - 1 = 0

Solution

x = W_{0} (e^{3}) - 2

+1

Decimal Notation

x = 0.20794 \dots

Solution steps

(x + 2) e^{x - 1} - 1 = 0

Prepare

(x + 2) e^{x - 1} - 1 = 0

for Lambert form:

(x + 2) e^{x - 1} = 1

Rewrite the equation with

x + 2 = u

and

x = u - 2

((u - 2) + 2) e^{(u - 2) - 1} = 1

Simplify

e^{u - 3} u = 1

Rewrite

e^{u - 3} u = 1

in Lambert form:

e^{u} u = e^{3}

Solve

e^{u} u = e^{3} : u = W_{0} (e^{3})

u = W_{0} (e^{3})

Substitute back

u = x + 2,

solve for

x

Solve

x + 2 = W_{0} (e^{3}) : x = W_{0} (e^{3}) - 2

x = W_{0} (e^{3}) - 2

Popular Examples

2^{3^{8^x}}=512

2^{3^{8^{x}}} = 512

6^{x} = 1

2 x = 4 2^{x} - 1

2^x=10^2+10^2-14^2

2^{x} = 1 0^{2} + 1 0^{2} - 1 4^{2}

solvefor x,e^x=(e^{11})/(e^y)solve for

x, e^{x} = \frac{e ^{11}}{e ^{y}}

Frequently Asked Questions (FAQ)

What is the answer to (x+2)e^{x-1}-1=0 ?
The answer to (x+2)e^{x-1}-1=0 is x=\W_{0}(e^3)-2