What is ln((sqrt(8u+3))/(8u-3)) ?

The solution to ln((sqrt(8u+3))/(8u-3)) is ln(sqrt(8u+3))-ln(8u-3)

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simplify ln((sqrt(8u+3))/(8u-3))

simplify

ln (\frac{8 u + 3}{8 u - 3})

ln (8 u + 3) - ln (8 u - 3)

Solution steps

ln (\frac{8 u + 3}{8 u - 3})

Apply log rule:

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

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

= ln (8 u + 3) - ln (8 u - 3)

e^{x + l n (x)} + ln (\frac{1}{x ^{3}})

lo g_{5} (7 \cdot 11)

- 12 (\frac{1}{2} ln ∣ 8 x - 8 ∣ - \frac{1}{2} ln ∣ 8 x - 10 ∣) + C

- \frac{1}{40} ln (\frac{1}{10})

\frac{1}{2} lo g_{5} (12)

What is ln((sqrt(8u+3))/(8u-3)) ?
The solution to ln((sqrt(8u+3))/(8u-3)) is ln(sqrt(8u+3))-ln(8u-3)