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

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

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

The solution is x=-\W_{-1}(-1/3),x=-\W_{0}(-1/3)

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2 x = 2 ln (3 x)

x = - W_{- 1} (- \frac{1}{3}), x = - W_{0} (- \frac{1}{3})

Decimal Notation

x = 1.51213 \dots, x = 0.61906 \dots

Solution steps

2 x = 2 ln (3 x)

Switch sides

2 ln (3 x) = 2 x

Divide both sides by

2

ln (3 x) = x

f (x) = g (x),

then

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

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

Simplify

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

3 x = e^{x}

Solve

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

x = - W_{- 1} (- \frac{1}{3}), x = - W_{0} (- \frac{1}{3})

Verify Solutions:

x = - W_{- 1} (- \frac{1}{3})

True

, x = - W_{0} (- \frac{1}{3})

True

The solutions are

x = - W_{- 1} (- \frac{1}{3}), x = - W_{0} (- \frac{1}{3})

lo g_{9} (x) = lo g_{3} (x)

ln (8^{x} - 1) = 0

6 lo g_{10} (2 x) = - 1

- 6 lo g_{2} (n) = - 24

y, ln (y) = n ln (x) + c

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