What is the answer to 2ln(3x)-x=0 ?

The answer to 2ln(3x)-x=0 is x=-2\W_{-1}(-1/6),x=-2\W_{0}(-1/6)

Solve for x: 2ln(3x)-x=0

The solution is x=-2\W_{-1}(-1/6),x=-2\W_{0}(-1/6)

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2 ln (3 x) - x = 0

x = - 2 W_{- 1} (- \frac{1}{6}), x = - 2 W_{0} (- \frac{1}{6})

Decimal Notation

x = 5.66629 \dots, x = 0.40896 \dots

Solution steps

2 ln (3 x) - x = 0

Move

x

to the right side

2 ln (3 x) = x

Divide both sides by

2

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

f (x) = g (x),

then

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

e^{l n (3 x)} = e^{\frac{x}{2}}

Simplify

e^{l n (3 x)} : 3 x

3 x = e^{\frac{x}{2}}

Solve

3 x = e^{\frac{x}{2}} : x = - 2 W_{- 1} (- \frac{1}{6}), x = - 2 W_{0} (- \frac{1}{6})

x = - 2 W_{- 1} (- \frac{1}{6}), x = - 2 W_{0} (- \frac{1}{6})

Verify Solutions:

x = - 2 W_{- 1} (- \frac{1}{6})

True

, x = - 2 W_{0} (- \frac{1}{6})

True

The solutions are

x = - 2 W_{- 1} (- \frac{1}{6}), x = - 2 W_{0} (- \frac{1}{6})

ln (x) = 3.27

lo g_{5} (8 x) - lo g_{5} (2) = 0

lo g_{3} (9 x \cdot 8) = 5

ln (x) = 3.43

lo g_{2} (2^{x + 1} - 8) = x

What is the answer to 2ln(3x)-x=0 ?
The answer to 2ln(3x)-x=0 is x=-2\W_{-1}(-1/6),x=-2\W_{0}(-1/6)
Solve for x: 2ln(3x)-x=0
The solution is x=-2\W_{-1}(-1/6),x=-2\W_{0}(-1/6)