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

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

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

simplify

\frac{1}{6} (ln ∣ x ∣ - ln (x + 6))

\frac{1}{6} ln (\frac{∣ x ∣}{x + 6})

Solution steps

\frac{1}{6} (ln ∣ x ∣ - ln (x + 6))

Apply log rule:

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

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

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

2 ln (x) - 4 lo g_{e} (\frac{1}{y}) - 3 lo g_{e} (x) y

3 ln (5) - \frac{1}{2} ln (4) + ln (8)

lo g_{4} (\frac{4 a}{b})

10.64 + lo g_{10} (\frac{0.13}{0.25})

- (ln (x + 1) + ln (x + 2))

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