What is expand ln(3/(2x^2y)) ?

The solution to expand ln(3/(2x^2y)) is ln(3)-ln(2)-2ln(x)-ln(y)

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expand ln(3/(2x^2y))

expand

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

ln (3) - ln (2) - 2 ln (x) - ln (y)

Solution steps

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

Apply log rule:

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

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

= ln (3) - ln (2 x^{2} y)

Apply log rule:

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

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

= ln (3) - (ln (x^{2}) + ln (y) + ln (2))

Apply log rule:

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

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

= ln (3) - (ln (2) + 2 ln (x) + ln (y))

- (ln (2) + 2 ln (x) + ln (y)) : - ln (2) - 2 ln (x) - ln (y)

= ln (3) - ln (2) - 2 ln (x) - ln (y)

lo g_{10} (\frac{x ^{6} y ^{9}}{z ^{2}})

- \frac{1}{4} ln (\frac{17}{34})

ln (\frac{0.0512}{0.32})

ln (3 x + 1) + ln (x - 1)

2 ln (2 x e^{β}) + e^{β} + 3 x

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