What is (-ln|4x+4|+ln|4x+2|)/2 ?

The solution to (-ln|4x+4|+ln|4x+2|)/2 is (ln((|4x+2|)/(|4x+4|)))/2

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simplify (-ln|4x+4|+ln|4x+2|)/2

simplify

\frac{- ln ∣ 4 x + 4 ∣ + ln ∣ 4 x + 2 ∣}{2}

\frac{ln ( \frac{∣ 4 x + 2 ∣}{∣ 4 x + 4 ∣} )}{2}

Solution steps

\frac{- ln ∣ 4 x + 4 ∣ + ln ∣ 4 x + 2 ∣}{2}

Apply log rule:

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

ln ∣ 4 x + 2 ∣ - ln ∣ 4 x + 4 ∣ = ln (\frac{∣ 4 x + 2 ∣}{∣ 4 x + 4 ∣})

= \frac{ln ( \frac{∣ 4 x + 2 ∣}{∣ 4 x + 4 ∣} )}{2}

3 lo g_{b} (y) - \frac{1}{4} lo g_{b} (w) + 2 lo g_{b} (z)

- ln (\frac{1}{1 + e ^{θ}})

3 ln (x + 1) - 3 ln (2) - 6 ln (x)

ln (0.764705 \cdot 1 0^{- 11})

\frac{1}{12} ln (\frac{2 x - 3}{2 x + 3})

What is (-ln|4x+4|+ln|4x+2|)/2 ?
The solution to (-ln|4x+4|+ln|4x+2|)/2 is (ln((|4x+2|)/(|4x+4|)))/2