simplify ln(x^3y^2)

Solution

simplify

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

3 ln (x) + 2 ln (y)

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

= 3 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)

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

lo g_{b} (A b)

ln (3 e^{2 x})

lo g_{5} (\frac{6}{27}) + lo g_{5} (\frac{3}{2})

lo g_{5} (\frac{z}{125})