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Popular >

x/(e^{3-2x)}=4

Solution

\frac{x}{e ^{3 - 2 x}} = 4

Solution

x = \frac{W _{0} ( 8 e ^{3} )}{2}

+1

Decimal Notation

x = 1.87803 \dots

Solution steps

\frac{x}{e ^{3 - 2 x}} = 4

Prepare

\frac{x}{e ^{3 - 2 x}} = 4

for Lambert form:

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

Rewrite the equation with

2 x = u

and

x = \frac{u}{2}

(\frac{u}{2}) e^{- 3 + 2 (\frac{u}{2})} = 4

Simplify

\frac{e ^{- 3 + u} u}{2} = 4

Rewrite

\frac{e ^{- 3 + u} u}{2} = 4

in Lambert form:

e^{u} u = 8 e^{3}

Solve

e^{u} u = 8 e^{3} : u = W_{0} (8 e^{3})

u = W_{0} (8 e^{3})

Substitute back

u = 2 x,

solve for

x

Solve

2 x = W_{0} (8 e^{3}) : x = \frac{W _{0} ( 8 e ^{3} )}{2}

x = \frac{W _{0} ( 8 e ^{3} )}{2}

Verify Solutions:

x = \frac{W _{0} ( 8 e ^{3} )}{2}

True

The solution is

x = \frac{W _{0} ( 8 e ^{3} )}{2}

Verify Solutions:

x = \frac{W _{0} ( 8 e ^{3} )}{2}

True

The solution is

x = \frac{W _{0} ( 8 e ^{3} )}{2}

Popular Examples

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y, x = 6^{y}

x 2^{3 x - 1} = 4^{x}

4^{3x+1}=6^{1-2x}

4^{3 x + 1} = 6^{1 - 2 x}

5^{x - 9} = 3

1.0 9^{x} = 1.5

Frequently Asked Questions (FAQ)

What is the answer to x/(e^{3-2x)}=4 ?
The answer to x/(e^{3-2x)}=4 is x=(\W_{0}(8e^3))/2