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

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

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

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

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

x = - 2 W_{- 1} (- \frac{1}{2 e}), x = - 2 W_{0} (- \frac{1}{2 e})

Decimal Notation

x = 5.35669 \dots, x = 0.46392 \dots

Solution steps

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

Move

\frac{1}{2} x

to the right side

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

Move

1

to the right side

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

f (x) = g (x),

then

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

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

Simplify

e^{l n (x)} : x

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

Solve

x = e^{\frac{1}{2} x - 1} : x = - 2 W_{- 1} (- \frac{1}{2 e}), x = - 2 W_{0} (- \frac{1}{2 e})

x = - 2 W_{- 1} (- \frac{1}{2 e}), x = - 2 W_{0} (- \frac{1}{2 e})

Verify Solutions:

x = - 2 W_{- 1} (- \frac{1}{2 e})

True

, x = - 2 W_{0} (- \frac{1}{2 e})

True

The solutions are

x = - 2 W_{- 1} (- \frac{1}{2 e}), x = - 2 W_{0} (- \frac{1}{2 e})

lo g_{3} (x + 1) + 10 = 10

lo g_{4} (2 x - 6) = lo g_{4} (4^{2})

lo g_{6} (x^{2} - 28) = 2

ln (x) = c (ln (4))^{2}

- ln (4 - z^{2}) + c = 0

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