simplify ln(x^6y^3)

Solution

simplify

ln (x^{6} y^{3})

6 ln (x) + 3 ln (y)

Solution steps

ln (x^{6} y^{3})

Apply log rule:

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

ln (x^{6} y^{3}) = ln (x^{6}) + ln (y^{3})

= ln (x^{6}) + ln (y^{3})

Apply log rule:

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

ln (x^{6}) = 6 ln (x)

= 6 ln (x) + ln (y^{3})

Apply log rule:

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

ln (y^{3}) = 3 ln (y)

= 6 ln (x) + 3 ln (y)

- lo g_{10} (2 \cdot 1 0^{- 3})

ln (x) + ln (x - 10)

- lo g_{10} (2 \cdot 1 0^{- 5})

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

lo g_{6} (k^{2} - 36) - lo g_{6} (k) - 6