What is the answer to 2x+3^x=13 ?

The answer to 2x+3^x=13 is x=-(2\W_{0}((e^{\frac{13ln(3))/2}ln(3))/(2))-13ln(3)}{2ln(3)}

Solve for x: 2x+3^x=13

The solution is x=-(2\W_{0}((e^{\frac{13ln(3))/2}ln(3))/(2))-13ln(3)}{2ln(3)}

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2 x + 3^{x} = 13

x = - \frac{2 W _{0} ( \frac{e ^{\frac{13 l n ( 3 )}{2}} l n ( 3 )}{2} ) - 13 ln ( 3 )}{2 ln ( 3 )}

Decimal Notation

x = 2

Solution steps

2 x + 3^{x} = 13

Prepare

2 x + 3^{x} = 13

for Lambert form:

1 = (13 - 2 x) e^{- l n (3) x}

Rewrite the equation with

(- x + \frac{13}{2}) ln (3) = u

and

x = - \frac{2 u - 13 ln ( 3 )}{2 ln ( 3 )}

1 = (13 - 2 (- \frac{2 u - 13 ln ( 3 )}{2 ln ( 3 )})) e^{- l n (3) (- \frac{2 u - 13 l n ( 3 )}{2 l n ( 3 )})}

Simplify

1 = e^{\frac{2 u - 13 l n ( 3 )}{2}} (13 + \frac{2 u - 13 ln ( 3 )}{ln ( 3 )})

Rewrite

1 = e^{\frac{2 u - 13 l n ( 3 )}{2}} (13 + \frac{2 u - 13 ln ( 3 )}{ln ( 3 )})

in Lambert form:

e^{u} u = \frac{e ^{\frac{13 l n ( 3 )}{2}} ln ( 3 )}{2}

Solve

e^{u} u = \frac{e ^{\frac{13 l n ( 3 )}{2}} ln ( 3 )}{2} : u = W_{0} (\frac{e ^{\frac{13 l n ( 3 )}{2}} ln ( 3 )}{2})

u = W_{0} (\frac{e ^{\frac{13 l n ( 3 )}{2}} ln ( 3 )}{2})

Substitute back

u = (- x + \frac{13}{2}) ln (3),

solve for

x

Solve

(- x + \frac{13}{2}) ln (3) = W_{0} (\frac{e ^{\frac{13 l n ( 3 )}{2}} ln ( 3 )}{2}) : x = - \frac{2 W _{0} ( \frac{e ^{\frac{13 l n ( 3 )}{2}} l n ( 3 )}{2} ) - 13 ln ( 3 )}{2 ln ( 3 )}

x = - \frac{2 W _{0} ( \frac{e ^{\frac{13 l n ( 3 )}{2}} l n ( 3 )}{2} ) - 13 ln ( 3 )}{2 ln ( 3 )}

(\frac{9}{7})^{3} \cdot (\frac{49}{81})^{2 x - 6} = (\frac{7}{9})^{9}

(\frac{x}{10}) - 20.89 \cdot e^{\frac{- x}{( 2478.82 )}} = 0

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

2^{n - 1} = 16

14 e^{6 - x} + e^{12 x - 7} = 0

What is the answer to 2x+3^x=13 ?
The answer to 2x+3^x=13 is x=-(2\W_{0}((e^{\frac{13ln(3))/2}ln(3))/(2))-13ln(3)}{2ln(3)}
Solve for x: 2x+3^x=13
The solution is x=-(2\W_{0}((e^{\frac{13ln(3))/2}ln(3))/(2))-13ln(3)}{2ln(3)}