What is the answer to x/2 ln(3x-1)=0 ?

The answer to x/2 ln(3x-1)=0 is x= 2/3

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x/2 ln(3x-1)=0

\frac{x}{2} ln (3 x - 1) = 0

x = \frac{2}{3}

Decimal Notation

x = 0.66666 \dots

Solution steps

\frac{x}{2} ln (3 x - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

\frac{x}{2} = 0 or ln (3 x - 1) = 0

Solve

\frac{x}{2} = 0 : x = 0

Solve

ln (3 x - 1) = 0 : x = \frac{2}{3}

Verify Solutions:

x = 0

False

, x = \frac{2}{3}

True

The solution is

x = \frac{2}{3}

lo g_{x} (\frac{1}{16}) = - 8

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

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

lo g_{8} (x) = - \frac{2}{3}

ln (4^{x}) = ln (e^{5 x - 1})