What is 1/3 (2ln(x)+ln(y)-2ln(z)) ?

The solution to 1/3 (2ln(x)+ln(y)-2ln(z)) is 1/3 ln((x^2y)/(z^2))

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simplify 1/3 (2ln(x)+ln(y)-2ln(z))

simplify

\frac{1}{3} (2 ln (x) + ln (y) - 2 ln (z))

\frac{1}{3} ln (\frac{x ^{2} y}{z ^{2}})

Solution steps

\frac{1}{3} (2 ln (x) + ln (y) - 2 ln (z))

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

= \frac{1}{3} (ln (x^{2}) + ln (y) - 2 ln (z))

Apply log rule:

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

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

= \frac{1}{3} (ln (x^{2} y) - 2 ln (z))

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

= \frac{1}{3} (- ln (z^{2}) + ln (x^{2} y))

Apply log rule:

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

ln (x^{2} y) - ln (z^{2}) = ln (\frac{x ^{2} y}{z ^{2}})

= \frac{1}{3} ln (\frac{x ^{2} y}{z ^{2}})

\frac{1}{2} ln (\frac{1 + sin ( x )}{1 - sin ( x )})

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

20 ln (\frac{1400}{1400 + 100 ( 10 )}) + 9.8 (10)

lo g_{x} (- 2 lo g_{y} (+ 5 lo g_{z} (x)))

ln (a \cdot \frac{a}{a + 5})

What is 1/3 (2ln(x)+ln(y)-2ln(z)) ?
The solution to 1/3 (2ln(x)+ln(y)-2ln(z)) is 1/3 ln((x^2y)/(z^2))