simplify ln(x^2y^3)

Solution

simplify

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

2 ln (x) + 3 ln (y)

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

= 2 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)

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

lo g_{3} (u) + 5 lo g_{3} (v)

ln (3 e^{- 2 x})

- lo g_{10} (8 \cdot 1 0^{- 2})

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

- lo g_{10} (2.5 x 1 0^{- 4})