simplify ln(4e^i)

Solution

simplify

ln (4 e^{i})

2 ln (2) + i

Solution steps

ln (4 e^{i})

Apply log rule:

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

ln (4 e^{i}) = ln (4) + ln (e^{i})

= ln (4) + ln (e^{i})

Apply log rule:

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

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

= ln (4) + i ln (e)

i ln (e) = i

= ln (4) + i

ln (4) = 2 ln (2)

= 2 ln (2) + i

ln (\frac{10000}{1000000})

ln (60 e^{\frac{x}{3}}) - ln (e^{\frac{x}{2}})

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

ln (\frac{∣ 8 + 2 x ∣}{∣ - 2 + 2 x ∣})

2 (2 ln ∣ x + 2 ∣ - ln ∣ x + 1 ∣)