What is the answer to 1+1/x-2*ln(x)=0 ?

The answer to 1+1/x-2*ln(x)=0 is x= 1/(2\W_{0)(1/(2e^{1/2)})}

Solve for x: 1+1/x-2*ln(x)=0

The solution is x= 1/(2\W_{0)(1/(2e^{1/2)})}

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1 + \frac{1}{x} - 2 \cdot ln (x) = 0

x = \frac{1}{2 W _{0} ( \frac{1}{2 e ^{\frac{1}{2}}} )}

Decimal Notation

x = 2.09349 \dots

Solution steps

1 + \frac{1}{x} - 2 ln (x) = 0

Move

\frac{1}{x}

to the right side

1 - 2 ln (x) = - \frac{1}{x}

Move

1

to the right side

- 2 ln (x) = - \frac{1}{x} - 1

Divide both sides by

- 2

ln (x) = - \frac{- 1 - x}{2 x}

f (x) = g (x),

then

a^{f (x)} = a^{g (x)}

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

Simplify

e^{l n (x)} : x

x = e^{- \frac{- 1 - x}{2 x}}

Solve

x = e^{- \frac{- 1 - x}{2 x}} : x = \frac{1}{2 W _{0} ( \frac{1}{2 e ^{\frac{1}{2}}} )}

x = \frac{1}{2 W _{0} ( \frac{1}{2 e ^{\frac{1}{2}}} )}

Verify Solutions:

x = \frac{1}{2 W _{0} ( \frac{1}{2 e ^{\frac{1}{2}}} )}

True

The solution is

x = \frac{1}{2 W _{0} ( \frac{1}{2 e ^{\frac{1}{2}}} )}

x, ln (x) = - 0.123

x + 2 x ln (x) = 0

3 ln (p) - 2 lo g_{p} (e) = 4

ln (x) = 7.1205

lo g_{2} (x + 2) = e

What is the answer to 1+1/x-2*ln(x)=0 ?
The answer to 1+1/x-2*ln(x)=0 is x= 1/(2\W_{0)(1/(2e^{1/2)})}
Solve for x: 1+1/x-2*ln(x)=0
The solution is x= 1/(2\W_{0)(1/(2e^{1/2)})}