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Popular >

2^x=2x

Solution

2^{x} = 2 x

Solution

x = 2, x = 1

Solution steps

2^{x} = 2 x

Prepare

2^{x} = 2 x

for Lambert form:

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

Rewrite the equation with

- x ln (2) = u

and

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

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

Simplify

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

Rewrite

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

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

2^{x} = 81

2^{x} = 29

4 (8^{x}) = 64

(1/2)^{x-1}=2^{3x-4}

(\frac{1}{2})^{x - 1} = 2^{3 x - 4}

6^{2 x} = 3 \cdot 2^{x}

Frequently Asked Questions (FAQ)

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