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Popular >

2^x=-x+6

Solution

2^{x} = - x + 6

Solution

x = 2

Solution steps

2^{x} = - x + 6

Prepare

2^{x} = - x + 6

for Lambert form:

1 = (- x + 6) e^{- l n (2) x}

Rewrite the equation with

(- x + 6) ln (2) = u

and

x = - \frac{u - 6 ln ( 2 )}{ln ( 2 )}

1 = (- (- \frac{u - 6 ln ( 2 )}{ln ( 2 )}) + 6) e^{- l n (2) (- \frac{u - 6 l n ( 2 )}{l n ( 2 )})}

Simplify

1 = e^{u - 6 l n (2)} (\frac{u - 6 ln ( 2 )}{ln ( 2 )} + 6)

Rewrite

1 = e^{u - 6 l n (2)} (\frac{u - 6 ln ( 2 )}{ln ( 2 )} + 6)

in Lambert form:

e^{u} u = 64 ln (2)

Solve

e^{u} u = 64 ln (2) : u = 4 ln (2)

u = 4 ln (2)

Substitute back

u = (- x + 6) ln (2),

solve for

x

Solve

(- x + 6) ln (2) = 4 ln (2) : x = 2

x = 2

Popular Examples

16 e^{4 x - 8} = 0

600 = 300 \cdot 6^{t}

e^{(- x + 4)} = 0

solvefor x,-e^{-x+4}+1=0.9 solve for

x, - e^{- x + 4} + 1 = 0.9

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

8 1^{x - 1} = 3^{x^{2}}

Frequently Asked Questions (FAQ)

What is the answer to 2^x=-x+6 ?
The answer to 2^x=-x+6 is x=2
Solve for x: 2^x=-x+6
The solution is x=2