simplify ln(x^ay^b)

Solution

simplify

ln (x^{a} y^{b})

a ln (x) + b ln (y)

Solution steps

ln (x^{a} y^{b})

Apply log rule:

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

ln (x^{a} y^{b}) = ln (x^{a}) + ln (y^{b})

= ln (x^{a}) + ln (y^{b})

Apply log rule:

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

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

= a ln (x) + ln (y^{b})

Apply log rule:

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

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

= a ln (x) + b ln (y)

ln^{2} (t) + 2 \cdot ln (t)

\frac{1}{3} ln (\frac{\frac{1}{2}}{\frac{3}{4}})

8 lo g_{b} (x) + 7 lo g_{b} (z)

\frac{π}{8} ln (\frac{13}{5})

- [\frac{2}{6} lo g_{2} (\frac{2}{6}) + \frac{4}{6} lo g_{2} (\frac{4}{6})]