What is simplify-ln| 8/3+8/3 2|+ln| 2/3+8/3 2|+C ?

The solution to simplify-ln| 8/3+8/3 2|+ln| 2/3+8/3 2|+C is ln(3/4)+C

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simplify-ln| 8/3+8/3 2|+ln| 2/3+8/3 2|+C

simplify

- ln \frac{8}{3} + \frac{8}{3} 2 + ln \frac{2}{3} + \frac{8}{3} 2 + C

ln (\frac{3}{4}) + C

Solution steps

- ln \frac{8}{3} + \frac{8}{3} \cdot 2 + ln \frac{2}{3} + \frac{8}{3} \cdot 2 + C

Apply log rule:

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

ln \frac{2}{3} + 2 \cdot \frac{8}{3} - ln \frac{8}{3} + 2 \cdot \frac{8}{3} = ln (\frac{2 \cdot \frac{8}{3} + \frac{2}{3}}{\frac{8}{3} + 2 \cdot \frac{8}{3}})

= ln (\frac{2 \cdot \frac{8}{3} + \frac{2}{3}}{\frac{8}{3} + 2 \cdot \frac{8}{3}}) + C

\frac{\frac{2}{3} + \frac{8}{3} \cdot 2}{\frac{8}{3} + \frac{8}{3} \cdot 2} = \frac{3}{4}

= ln (\frac{3}{4}) + C

\frac{1}{2} lo g_{10} (n) + 3 lo g_{10} (m)

lo g_{u} (u^{- 7}) + 5 lo g_{u} (u^{\frac{2}{5}})

lo g_{2} (5) + lo g_{2} (6)

lo g_{b} (\frac{1.792}{1.946})

\frac{1}{4} lo g_{5} (16) + \frac{1}{5} lo g_{5} (243)

What is simplify-ln| 8/3+8/3 2|+ln| 2/3+8/3 2|+C ?
The solution to simplify-ln| 8/3+8/3 2|+ln| 2/3+8/3 2|+C is ln(3/4)+C