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Popular >

3^x+x=30

Solution

3^{x} + x = 30

Solution

x = 3

Solution steps

3^{x} + x = 30

Prepare

3^{x} + x = 30

for Lambert form:

1 = (30 - x) e^{- l n (3) x}

Rewrite the equation with

(- x + 30) ln (3) = u

and

x = - \frac{u - 30 ln ( 3 )}{ln ( 3 )}

1 = (30 - (- \frac{u - 30 ln ( 3 )}{ln ( 3 )})) e^{- l n (3) (- \frac{u - 30 l n ( 3 )}{l n ( 3 )})}

Simplify

1 = e^{u - 30 l n (3)} (30 + \frac{u - 30 ln ( 3 )}{ln ( 3 )})

Rewrite

1 = e^{u - 30 l n (3)} (30 + \frac{u - 30 ln ( 3 )}{ln ( 3 )})

in Lambert form:

e^{u} u = 3^{30} ln (3)

Solve

e^{u} u = 3^{30} ln (3) : u = 27 ln (3)

u = 27 ln (3)

Substitute back

u = (- x + 30) ln (3),

solve for

x

Solve

(- x + 30) ln (3) = 27 ln (3) : x = 3

x = 3

Popular Examples

xe^{2x}-xe^x-6x=0

x e^{2 x} - x e^{x} - 6 x = 0

e^{2 x} = e^{x} + 6

(100)/(1+15e^{-0.4x)}=20

\frac{100}{1 + 15 e ^{- 0.4 x}} = 20

3^{x-4}=8^{2x+2}

3^{x - 4} = 8^{2 x + 2}

2-3^{-x}+3^{x+1}=0

2 - 3^{- x} + 3^{x + 1} = 0

Frequently Asked Questions (FAQ)

What is the answer to 3^x+x=30 ?
The answer to 3^x+x=30 is x=3
Solve for x: 3^x+x=30
The solution is x=3