simplify ln(ab^n)

Solution

simplify

ln (a b^{n})

ln (a) + n ln (b)

Solution steps

ln (a b^{n})

Apply log rule:

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

ln (a b^{n}) = ln (a) + ln (b^{n})

= ln (a) + ln (b^{n})

Apply log rule:

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

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

= ln (a) + n ln (b)

ln (1 - x) + ln (1 + x)

ln (\frac{2 y ^{2}}{z ^{3}})

- 0.3 \cdot lo g_{2} (0.3) - 0.7 \cdot lo g_{2} (0.7)

14.77 + 10 lo g_{10} (\frac{179.68}{1.905})

ln (100) - ln (5) + ln (4)