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

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

Solve for x: ln(3x)=x

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

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ln (3 x) = 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

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_{x + 6} (2 x^{2} - 4 x) = 2

lo g_{2} (x + 1) + lo g_{2} (x - 2) = 3

ln (x) = 900

lo g_{10} (x^{2} + 36) = 2

ln (x) = 5.014055365

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