simplify ln(-ie^3)

Solution

simplify

ln (- i e^{3})

ln (i) + 3

Solution steps

ln (- i e^{3})

Apply log rule:

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

ln (- i e^{3}) = ln (i) + ln (e^{3})

= ln (i) + ln (e^{3})

Apply log rule:

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

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

= ln (i) + 3 ln (e)

3 ln (e) = 3

= ln (i) + 3

- lo g_{10} (1.2 \cdot 1 0^{- 3})

lo g_{10} (\frac{x ^{4}}{y ^{5}})

ln (e \frac{1}{2})

ln (7) + ln (5)

\frac{1}{3} ln (16 p) - 3 ln (2 p) q - 2 ln (5) p^{4} + 6 ln (q)