What is ln((sqrt(z))/(xy)) ?

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

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simplify ln((sqrt(z))/(xy))

simplify

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

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

Solution steps

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

Apply log rule:

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

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

= ln (z) - ln (x y)

Apply log rule:

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

ln (x y) = ln (x) + ln (y)

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

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

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

lo g_{10} (\frac{x}{y ^{3}})

\frac{1}{2} lo g_{10} (a) - 3 lo g_{10} (b)

2 lo g_{10} (b) - \frac{1}{2} (lo g_{10} (c) + 4 lo g_{10} (d)) + 5 lo g_{10} (h)

3 ln (10) - 4 ln (2) - ln (5)

lo g_{10} (\frac{x ^{3} y ^{4}}{z ^{6}})

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