What is the answer to 3^{3-x}=x ?

The answer to 3^{3-x}=x is x=(\W_{0}(27ln(3)))/(ln(3))

Solve for x: 3^{3-x}=x

The solution is x=(\W_{0}(27ln(3)))/(ln(3))

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3^{3 - x} = x

x = \frac{W _{0} ( 27 ln ( 3 ) )}{ln ( 3 )}

Decimal Notation

x = 2.25844 \dots

Solution steps

3^{3 - x} = x

Prepare

3^{3 - x} = x

for Lambert form:

1 = x e^{l n (3) (- 3 + x)}

Rewrite the equation with

x ln (3) = u

and

x = \frac{u}{ln ( 3 )}

1 = (\frac{u}{ln ( 3 )}) e^{l n (3) (- 3 + (\frac{u}{l n ( 3 )}))}

Simplify

1 = \frac{e ^{- 3 l n (3) + u} u}{ln ( 3 )}

Rewrite

1 = \frac{e ^{- 3 l n (3) + u} u}{ln ( 3 )}

in Lambert form:

e^{u} u = 27 ln (3)

Solve

e^{u} u = 27 ln (3) : u = W_{0} (27 ln (3))

u = W_{0} (27 ln (3))

Substitute back

u = x ln (3),

solve for

x

Solve

x ln (3) = W_{0} (27 ln (3)) : x = \frac{W _{0} ( 27 ln ( 3 ) )}{ln ( 3 )}

x = \frac{W _{0} ( 27 ln ( 3 ) )}{ln ( 3 )}

8 1^{x + 1} + 3^{4 x} = 243

1 3^{9} x = 1 1^{x + 5}

9^{\frac{x - 1}{2}} = (3^{x})^{2}

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

2^{2 x + 1} - 15 (2^{x}) - 8 = 0

What is the answer to 3^{3-x}=x ?
The answer to 3^{3-x}=x is x=(\W_{0}(27ln(3)))/(ln(3))
Solve for x: 3^{3-x}=x
The solution is x=(\W_{0}(27ln(3)))/(ln(3))