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Popular >

xe^{3x}-1=3

Solution

x e^{3 x} - 1 = 3

Solution

x = \frac{W _{0} ( 12 )}{3}

+1

Decimal Notation

x = 0.62093 \dots

Solution steps

x e^{3 x} - 1 = 3

Prepare

x e^{3 x} - 1 = 3

for Lambert form:

x e^{3 x} = 4

Rewrite the equation with

3 x = u

and

x = \frac{u}{3}

(\frac{u}{3}) e^{u} = 4

Rewrite

(\frac{u}{3}) e^{u} = 4

in Lambert form:

e^{u} u = 12

Solve

e^{u} u = 12 : u = W_{0} (12)

u = W_{0} (12)

Substitute back

u = 3 x,

solve for

x

Solve

3 x = W_{0} (12) : x = \frac{W _{0} ( 12 )}{3}

x = \frac{W _{0} ( 12 )}{3}

Popular Examples

3. 4^{x} - 7 = 185

2^{x+7}=8^{x+2}

2^{x + 7} = 8^{x + 2}

e^{- x} = e^{x}

3^{3 x - 1} = 9

3^{x} = 2 x + 1

Frequently Asked Questions (FAQ)

What is the answer to xe^{3x}-1=3 ?
The answer to xe^{3x}-1=3 is x=(\W_{0}(12))/3