simplify ln(3xy^2)

Solution

simplify

ln (3 x y^{2})

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

Solution steps

ln (3 x y^{2})

Apply log rule:

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

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

= ln (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)

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

3 ln (x) + 2 ln (y) + ln (5)

lo g_{10} (\frac{4 x ^{3}}{y ^{2}})

lo g_{3} (20) - lo g_{3} (4)

ln (\frac{11}{16})

ln (\frac{3}{4}) - 1