simplify ln(xyz^2)

Solution

simplify

ln (x y z^{2})

ln (x) + ln (y) + 2 ln (z)

Solution steps

ln (x y z^{2})

Apply log rule:

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

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

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

Apply log rule:

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

ln (z^{2}) = 2 ln (z)

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

ln (2 + 1) - ln (2 - 1)

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

lo g_{7} (x) - lo g_{7} (x^{9})

ln (\frac{6}{e ^{4}})

lo g_{2} (x) - lo g_{2} (x^{6})