What is the answer to 1/2 x-3=ln(x)-1 ?

The answer to 1/2 x-3=ln(x)-1 is x=-2\W_{-1}(-1/(2e^2)),x=-2\W_{0}(-1/(2e^2))

Solve for x: 1/2 x-3=ln(x)-1

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

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

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

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

Switch sides

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

Move

1

to the right side

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}})

y, ln (y + 3) = 2 ln (x)

x \cdot 9^{l o g_{3} (x)} = 27

9 ln (0.25 x) = 15

1 = lo g_{6} (- 7 + 2 x)

3 lo g_{4} (x) = 12

What is the answer to 1/2 x-3=ln(x)-1 ?
The answer to 1/2 x-3=ln(x)-1 is x=-2\W_{-1}(-1/(2e^2)),x=-2\W_{0}(-1/(2e^2))
Solve for x: 1/2 x-3=ln(x)-1
The solution is x=-2\W_{-1}(-1/(2e^2)),x=-2\W_{0}(-1/(2e^2))