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

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

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

simplify

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

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

Solution steps

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

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}) + C

Simplify

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

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

ln (\frac{( 2 x + 1 ) ^{\frac{1}{3}}}{( 3 x - 2 ) ^{\frac{1}{4}}})

ln (\frac{9}{19})

\frac{1}{5} lo g_{7} (x) + 6 lo g_{7} (w) - lo g_{7} (z)

lo g_{\frac{1}{2}} (\frac{3 x ^{2}}{2})

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