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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

ln (4) = 2 ln (2)

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

ln (\frac{12}{12 + d})

2 - 2 ln (e + 1) + ln (4)

lo g_{2} (\frac{8 d ^{4}}{n ^{3}})

ln (2) - 4 - 2 ln (3)

e^{(3^{2} - 1)} \cdot 3^{3} + ln (5 \cdot 3^{3}) \cdot 3^{2} + 15

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