simplify ln(xy^2)

Solution

simplify

ln (x y^{2})

ln (x) + 2 ln (y)

Solution steps

ln (x y^{2})

Apply log rule:

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

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

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

Apply log rule:

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

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

= ln (x) + 2 ln (y)

2 lo g_{2} (10) - lo g_{2} (x)

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

ln (x^{3}) - ln (x)

lo g_{b} (\frac{x ^{3} y}{z ^{9}})

\frac{2}{5} ln (\frac{15}{4})