What is 1/24 ln(cos(3)x^2)+c ?

The solution to 1/24 ln(cos(3)x^2)+c is 1/24 ln(cos(3))+1/12 ln(x)+c

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simplify 1/24 ln(cos(3)x^2)+c

simplify

\frac{1}{24} ln (cos (3) x^{2}) + c

\frac{1}{24} ln (cos (3)) + \frac{1}{12} ln (x) + c

Solution steps

\frac{1}{24} ln (cos (3) x^{2}) + c

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

\frac{1}{24} ln (cos (3) x^{2}) = \frac{1}{24} ln (cos (3)) + \frac{1}{24} ln (x^{2})

= \frac{1}{24} ln (cos (3)) + \frac{1}{24} ln (x^{2}) + c

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (x^{2}) = 2 ln (x)

= \frac{1}{24} ln (cos (3)) + \frac{1}{24} \cdot 2 ln (x) + c

\frac{1}{24} \cdot 2 ln (x) = \frac{1}{12} ln (x)

= \frac{1}{24} ln (cos (3)) + \frac{1}{12} ln (x) + c

lo g_{a} (x^{3}) - lo g_{a} (x^{4}) + 2 lo g_{a} (x)

lo g_{10} (lo g_{10} (x^{4}) y)

\frac{1}{2} [3 ln (x + 3) + ln (x) - ln (x^{2} - 1)]

ln (\frac{10}{9.97})

6 lo g_{3} (w - 4) - 3 lo g_{3} (w + 3)

What is 1/24 ln(cos(3)x^2)+c ?
The solution to 1/24 ln(cos(3)x^2)+c is 1/24 ln(cos(3))+1/12 ln(x)+c