What is 1/3 ln(3r^2s) ?

The solution to 1/3 ln(3r^2s) is 1/3 ln(3)+2/3 ln(r)+1/3 ln(s)

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simplify 1/3 ln(3r^2s)

simplify

\frac{1}{3} ln (3 r^{2} s)

\frac{1}{3} ln (3) + \frac{2}{3} ln (r) + \frac{1}{3} ln (s)

Solution steps

\frac{1}{3} ln (3 r^{2} s)

Apply log rule:

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

\frac{1}{3} ln (3 r^{2} s) = \frac{1}{3} ln (3) + \frac{1}{3} ln (r^{2}) + \frac{1}{3} ln (s)

= \frac{1}{3} ln (3) + \frac{1}{3} ln (r^{2}) + \frac{1}{3} ln (s)

Apply log rule:

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

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

= \frac{1}{3} ln (3) + \frac{1}{3} \cdot 2 ln (r) + \frac{1}{3} ln (s)

\frac{1}{3} \cdot 2 ln (r) = \frac{2}{3} ln (r)

= \frac{1}{3} ln (3) + \frac{2}{3} ln (r) + \frac{1}{3} ln (s)

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\frac{ln ( 1.19 ) - ln ( 1.17 )}{2}

ln (3) + ln (- 1)

(32) ln (\frac{0.6}{0.3})

What is 1/3 ln(3r^2s) ?
The solution to 1/3 ln(3r^2s) is 1/3 ln(3)+2/3 ln(r)+1/3 ln(s)