What is 1/4 (ln|(x+5)/2+1|-ln|(x+5)/2-1|) ?

The solution to 1/4 (ln|(x+5)/2+1|-ln|(x+5)/2-1|) is 1/4 ln((|x+7|)/(|x+3|))

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simplify 1/4 (ln|(x+5)/2+1|-ln|(x+5)/2-1|)

simplify

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

\frac{1}{4} ln (\frac{∣ x + 7 ∣}{∣ x + 3 ∣})

Solution steps

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

Apply log rule:

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

ln \frac{x + 5}{2} + 1 - ln \frac{x + 5}{2} - 1 = ln (\frac{\frac{x + 5}{2} + 1}{\frac{x + 5}{2} - 1})

= \frac{1}{4} ln (\frac{\frac{x + 5}{2} + 1}{\frac{x + 5}{2} - 1})

Simplify

\frac{\frac{x + 5}{2} + 1}{\frac{x + 5}{2} - 1} : \frac{∣ x + 7 ∣}{∣ x + 3 ∣}

= \frac{1}{4} ln (\frac{∣ x + 7 ∣}{∣ x + 3 ∣})

lo g_{10} (θ^{x} (1 - θ)^{(1 - x)})

lo g_{y} (\frac{x}{8})

ln (\frac{2 x}{y ^{10}})

2 ln (2 + 3) - 2 ln (2 - 3)

ln (\frac{x ^{3.9644} e ^{- x}}{3.9644 !})

What is 1/4 (ln|(x+5)/2+1|-ln|(x+5)/2-1|) ?
The solution to 1/4 (ln|(x+5)/2+1|-ln|(x+5)/2-1|) is 1/4 ln((|x+7|)/(|x+3|))