What is ln((3xy^2)/z) ?

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

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simplify ln((3xy^2)/z)

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

\frac{1}{3} ln ∣ x - 3 ∣ + \frac{1}{3} ln x^{2} + 9

ln (\frac{1 + e ^{- x}}{2 - 3 x})

ln (\frac{r ^{2} s ^{11}}{t ^{14}})

\frac{1}{5} ln (x + 1) + \frac{4}{5} ln (x - 4)

5 lo g_{7} (y) - \frac{3}{5} lo g_{7} (z)

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