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

The solution to simplify-1/4 (ln| x/2+1|-ln| x/2-1|) is -1/4 ln((|x+2|)/(|x-2|))

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Simplify

\frac{\frac{x}{2} + 1}{\frac{x}{2} - 1} : \frac{∣ x + 2 ∣}{∣ x - 2 ∣}

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

lo g_{x} (2 y)

\frac{100}{9} ln (\frac{3.8}{4})

lo g_{6} ((\frac{8 \cdot 7}{3 ^{5}})^{4})

ln u^{2} - 3 u + 1 + 2 ln ∣ y ∣

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

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