What is ln((sqrt(z))/(x^2y)) ?

The solution to ln((sqrt(z))/(x^2y)) is ln(sqrt(z))-2ln(x)-ln(y)

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simplify ln((sqrt(z))/(x^2y))

simplify

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

ln (z) - 2 ln (x) - ln (y)

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

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

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

ln (x) + ln (y^{- 1})

5 - 10 ln (\frac{3}{2})

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

ln (7 b \frac{b + 6}{b - 6})

5 lo g_{10} (x) - lo g_{10} (y)

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