What is simplify-1/8 (ln|a+5/2 |-ln|a+1/2 |)+C ?

The solution to simplify-1/8 (ln|a+5/2 |-ln|a+1/2 |)+C is -1/8 ln((|2a+5|)/(|2a+1|))+C

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simplify-1/8 (ln|a+5/2 |-ln|a+1/2 |)+C

simplify

- \frac{1}{8} (ln a + \frac{5}{2} - ln a + \frac{1}{2}) + C

- \frac{1}{8} ln (\frac{∣ 2 a + 5 ∣}{∣ 2 a + 1 ∣}) + C

Solution steps

- \frac{1}{8} (ln a + \frac{5}{2} - ln a + \frac{1}{2}) + C

Apply log rule:

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

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

= - \frac{1}{8} ln (\frac{a + \frac{5}{2}}{a + \frac{1}{2}}) + C

Simplify

\frac{a + \frac{5}{2}}{a + \frac{1}{2}} : \frac{∣ 2 a + 5 ∣}{∣ 2 a + 1 ∣}

= - \frac{1}{8} ln (\frac{∣ 2 a + 5 ∣}{∣ 2 a + 1 ∣}) + C

ln (\frac{10}{22}) \cdot 5

ln (a \cdot b \cdot c)

- ln (5) - \frac{1}{4} ln (3)

ln (\frac{( x ^{5} \cdot z ^{5} )}{y ^{11} \cdot w ^{15}})

\frac{5 ln ( 7 )}{3 ln ( 10 ) - ln ( 7 )}

What is simplify-1/8 (ln|a+5/2 |-ln|a+1/2 |)+C ?
The solution to simplify-1/8 (ln|a+5/2 |-ln|a+1/2 |)+C is -1/8 ln((|2a+5|)/(|2a+1|))+C