What is 1/3 ln((|sqrt(9x^2-16)+3x|)/4)+C ?

The solution to 1/3 ln((|sqrt(9x^2-16)+3x|)/4)+C is 1/3 (ln|sqrt(9x^2-16)+3x|-2ln(2))+C

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simplify 1/3 ln((|sqrt(9x^2-16)+3x|)/4)+C

simplify

\frac{1}{3} ln (\frac{9 x ^{2} - 16 + 3 x}{4}) + C

\frac{1}{3} (ln 9 x^{2} - 16 + 3 x - 2 ln (2)) + C

Solution steps

\frac{1}{3} ln (\frac{9 x ^{2} - 16 + 3 x}{4}) + C

Apply log rule:

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

ln (\frac{9 x ^{2} - 16 + 3 x}{4}) = ln 9 x^{2} - 16 + 3 x - ln (4)

= \frac{1}{3} (ln 3 x + 9 x^{2} - 16 - ln (4)) + C

ln (4) = 2 ln (2)

= \frac{1}{3} (ln 3 x + 9 x^{2} - 16 - 2 ln (2)) + C

ln (20000 \cdot 10000)

ln (294) - ln (51.5)

2 [2 ln (x) - ln (x + 4) - ln (x - 4)]

3 lo g_{2} (x) - lo g_{2} (y)

- lo g_{10} (5.16 \cdot 1 0^{- 6})

What is 1/3 ln((|sqrt(9x^2-16)+3x|)/4)+C ?
The solution to 1/3 ln((|sqrt(9x^2-16)+3x|)/4)+C is 1/3 (ln|sqrt(9x^2-16)+3x|-2ln(2))+C