simplify ln(x^5y^8)

Solution

simplify

ln (x^{5} y^{8})

5 ln (x) + 8 ln (y)

Solution steps

ln (x^{5} y^{8})

Apply log rule:

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

ln (x^{5} y^{8}) = ln (x^{5}) + ln (y^{8})

= ln (x^{5}) + ln (y^{8})

Apply log rule:

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

ln (x^{5}) = 5 ln (x)

= 5 ln (x) + ln (y^{8})

Apply log rule:

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

ln (y^{8}) = 8 ln (y)

= 5 ln (x) + 8 ln (y)

ln (\frac{x ^{4} y}{3 z ^{5}})

ln (x^{3} 2 - x)

3 lo g_{10} (x) - 6 lo g_{10} (x + 1)

ln (4) + 2 ln (x) + 3 ln (x^{2} + 3)

7 lo g_{3} (a) + 2 lo g_{3} (b) - \frac{1}{2} lo g_{3} (2 c)