simplify ln(x^3y^3)

Solution

simplify

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

3 ln (x) + 3 ln (y)

Solution steps

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

Apply log rule:

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

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

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

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^{3})

Apply log rule:

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

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

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

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

2 lo g_{6} (u) + 6 lo g_{6} (v)

- 4 ln (x - 2) + 3 ln (1 - x)

2 lo g_{3} (x - y) - 3 lo g_{3} (m)

ln (A) - ln (B)