simplify ln(x^2(y))

Solution

simplify

ln (x^{2} (y))

2 ln (x) + ln (y)

Solution steps

ln (x^{2} (y))

Apply log rule:

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

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

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

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)

ln (\frac{121.306}{125})

ln (4) + 3 ln (x) + 5 ln (x^{2} + 10)

ln (6) - 3 ln (a) + ln (b)

u^{2} + 2 u - 4 ln (u) + 2 ln (y)

- 2 ln (\frac{y}{x} + 1)