simplify ln^3(ab^2)

Solution

simplify

ln^{3} (a b^{2})

ln^{3} (a) + 2 ln^{3} (b)

Solution steps

ln^{3} (a b^{2})

Apply log rule:

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

ln^{3} (a b^{2}) = ln^{3} (a) + ln^{3} (b^{2})

= ln^{3} (a) + ln^{3} (b^{2})

Apply log rule:

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

ln^{3} (b^{2}) = 2 ln^{3} (b)

= ln^{3} (a) + 2 ln^{3} (b)

ln (\frac{a + 1}{a})

ln_{3} (0.2) + ln_{3} (1215)

lo g_{10} (1215 x^{0.84})

ln (x) - 3 ln (z) + 0.5 ln (y)

lo g_{10} (x^{5} y^{3} z)