What is 1/6 (ln|3x+1|-ln|3x-1|) ?

The solution to 1/6 (ln|3x+1|-ln|3x-1|) is 1/6 ln((|3x+1|)/(|3x-1|))

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simplify 1/6 (ln|3x+1|-ln|3x-1|)

simplify

\frac{1}{6} (ln ∣ 3 x + 1 ∣ - ln ∣ 3 x - 1 ∣)

\frac{1}{6} ln (\frac{∣ 3 x + 1 ∣}{∣ 3 x - 1 ∣})

Solution steps

\frac{1}{6} (ln ∣ 3 x + 1 ∣ - ln ∣ 3 x - 1 ∣)

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln ∣ 3 x + 1 ∣ - ln ∣ 3 x - 1 ∣ = ln (\frac{∣ 3 x + 1 ∣}{∣ 3 x - 1 ∣})

= \frac{1}{6} ln (\frac{∣ 3 x + 1 ∣}{∣ 3 x - 1 ∣})

ln (\frac{15}{8})

ln (\frac{43 - 263}{21 - 263})

ln (\frac{393.62}{390.66}) - 1

ln (\frac{10.41}{3.75})

\frac{1}{2 2} ln (\frac{2 - 1}{2 + 1})

What is 1/6 (ln|3x+1|-ln|3x-1|) ?
The solution to 1/6 (ln|3x+1|-ln|3x-1|) is 1/6 ln((|3x+1|)/(|3x-1|))