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

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

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x=ln(-3x)

x = ln (- 3 x)

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

Decimal Notation

x = - 0.25762 \dots

Solution steps

x = ln (- 3 x)

f (x) = g (x),

then

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

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

Simplify

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

e^{x} = - 3 x

Solve

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

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

Verify Solutions:

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

True

The solution is

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

ln (x) + ln (2 x) = 8

ln (x) + ln (2 x) = 7

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

lo g_{3} (12 x) - 3 = lo g_{2} (540)

x = e^{l o g_{7} (x)}