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

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

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

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

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

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

Decimal Notation

x = 8.21093 \dots, x = 0.14555 \dots

Solution steps

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

f (x) = g (x),

then

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

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

Simplify

e^{l n (x)} : x

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

Solve

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

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

Verify Solutions:

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

True

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

True

The solutions are

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

4 lo g_{x} (2) = lo g_{2} (x)

lo g_{x + 6} (3 x^{2} + 6 x) = 2

ln (4 - x) = 0

ln (x + 6) = - 1

lo g_{a} (n^{a}) = n

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