What is expand ln((z^3)/(sqrt(xy))) ?

The solution to expand ln((z^3)/(sqrt(xy))) is 3ln(z)-ln(sqrt(xy))

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expand ln((z^3)/(sqrt(xy)))

expand

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

3 ln (z) - ln (x y)

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

ln (z^{3}) = 3 ln (z)

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

lo g_{10} (3 z) + 2 lo g_{10} (7)

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

lo g_{10} (2 x) + 3 lo g_{10} (2 y)

lo g_{10} (p) - \frac{1}{3} lo g_{10} (q)

ln (5) + \frac{1}{2} ln (9)

What is expand ln((z^3)/(sqrt(xy))) ?
The solution to expand ln((z^3)/(sqrt(xy))) is 3ln(z)-ln(sqrt(xy))