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Popular >

2x=2^x

Solution

2 x = 2^{x}

Solution

x = 2, x = 1

Solution steps

2 x = 2^{x}

Prepare

2 x = 2^{x}

for Lambert form:

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

Rewrite the equation with

- x ln (2) = u

and

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

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

Simplify

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

Rewrite

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

in Lambert form:

e^{u} u = - \frac{ln ( 2 )}{2}

Solve

e^{u} u = - \frac{ln ( 2 )}{2} : u = - 2 ln (2), u = - ln (2)

u = - 2 ln (2), u = - ln (2)

Substitute back

u = - x ln (2),

solve for

x

Solve

- x ln (2) = - 2 ln (2) : x = 2

Solve

- x ln (2) = - ln (2) : x = 1

x = 2, x = 1

Popular Examples

3^{-x+1}=9^{x+2}

3^{- x + 1} = 9^{x + 2}

4^{x} = 17

4^{x} = 12

4^{x + 2} = 3

e^{- x} = - 1

Frequently Asked Questions (FAQ)

What is the answer to 2x=2^x ?
The answer to 2x=2^x is x=2,x=1
Solve for x: 2x=2^x
The solution is x=2,x=1