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 ∣})

ln (2 x^{5})

- lo g_{10} (6.6 \cdot 1 0^{- 8})

ln (\frac{x - sin ( x )}{x + sin ( x )})

lo g_{2} ((x^{3} + 2) (x - 8)^{3})

ln (\frac{n ^{2} + 1}{2 n ^{2} + 1})

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|))