simplify ln(x^2y^5)

Solution

simplify

ln (x^{2} y^{5})

2 ln (x) + 5 ln (y)

Solution steps

ln (x^{2} y^{5})

Apply log rule:

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

ln (x^{2} y^{5}) = ln (x^{2}) + ln (y^{5})

= ln (x^{2}) + ln (y^{5})

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^{5})

Apply log rule:

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

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

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

lo g_{x} (x x)

ln (3.7) - ln (1.9)

lo g_{10} (7 x^{3})

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

ln (x) - ln (2 x)