What is the answer to 2^x+x=5 ?

The answer to 2^x+x=5 is x=-(\W_{0}(32ln(2))-5ln(2))/(ln(2))

The solution is x=-(\W_{0}(32ln(2))-5ln(2))/(ln(2))

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Popular >

2^x+x=5

Solution

2^{x} + x = 5

Solution

x = - \frac{W _{0} ( 32 ln ( 2 ) ) - 5 ln ( 2 )}{ln ( 2 )}

Decimal

x = 1.71562 \dots

Solution steps

2^{x} + x = 5

Prepare

2^{x} + x = 5

for Lambert form:

1 = (5 - x) e^{- l n (2) x}

Rewrite the equation with

(- x + 5) ln (2) = u

and

x = - \frac{u - 5 ln ( 2 )}{ln ( 2 )}

1 = (5 - (- \frac{u - 5 ln ( 2 )}{ln ( 2 )})) e^{- l n (2) (- \frac{u - 5 l n ( 2 )}{l n ( 2 )})}

Simplify

1 = e^{u - 5 l n (2)} (5 + \frac{u - 5 ln ( 2 )}{ln ( 2 )})

Rewrite

1 = e^{u - 5 l n (2)} (5 + \frac{u - 5 ln ( 2 )}{ln ( 2 )})

in Lambert form:

e^{u} u = 32 ln (2)

Solve

e^{u} u = 32 ln (2) : u = W_{0} (32 ln (2))

u = W_{0} (32 ln (2))

Substitute back

u = (- x + 5) ln (2),

solve for

x

Solve

(- x + 5) ln (2) = W_{0} (32 ln (2)) : x = - \frac{W _{0} ( 32 ln ( 2 ) ) - 5 ln ( 2 )}{ln ( 2 )}

x = - \frac{W _{0} ( 32 ln ( 2 ) ) - 5 ln ( 2 )}{ln ( 2 )}

Graph

Popular Examples

9^{x+2}=27^{-x}

9^{x + 2} = 2 7^{- x}

-24\times 3^{x-1}+9^x=9

- 24 \times 3^{x - 1} + 9^{x} = 9

7^{-x}=49

7^{- x} = 49

6=34.416e^{-0.18(t)}

6 = 34.416 e^{- 0.18 (t)}

(1+x^2)2^x-5*2^x=0

(1 + x^{2}) 2^{x} - 5 \cdot 2^{x} = 0

Frequently Asked Questions (FAQ)

What is the answer to 2^x+x=5 ?
The answer to 2^x+x=5 is x=-(\W_{0}(32ln(2))-5ln(2))/(ln(2))
Solve for x: 2^x+x=5
The solution is x=-(\W_{0}(32ln(2))-5ln(2))/(ln(2))

2^x+x=5

Solution

Solution

Graph

Popular Examples

Frequently Asked Questions (FAQ)

What is the answer to 2^x+x=5 ?

Solve for x: 2^x+x=5