What is ln((e^{i0})/(4+3e^{i0)}) ?

The solution to ln((e^{i0})/(4+3e^{i0)}) is -ln(7)

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simplify ln((e^{i0})/(4+3e^{i0)})

simplify

ln (\frac{e ^{i 0}}{4 + 3 e ^{i 0}})

- ln (7)

Decimal Notation

- 1.94591 \dots

Solution steps

ln (\frac{e ^{i 0}}{4 + 3 e ^{i 0}})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{e ^{i 0}}{4 + 3 e ^{i 0}}) = ln (e^{i 0}) - ln (4 + 3 e^{i 0})

= ln (e^{0 i}) - ln (3 e^{0 i} + 4)

Apply log rule:

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

ln (e^{i 0}) = i 0 \cdot ln (e)

= i 0 \cdot ln (e) - ln (4 + 3 e^{i 0})

i 0 \cdot ln (e) = 0

ln (4 + 3 e^{i 0}) = ln (7)

= 0 - ln (7)

0 - ln (7) = - ln (7)

= - ln (7)

\frac{7}{4} ln ∣ x ∣ - \frac{3}{4} ln ∣ x + 4 ∣

lo g_{3} (4 x) + lo g_{3} (\frac{x}{9})

ln (5 (7))

lo g_{b} (\frac{a}{c})

f (x) lo g_{3} (x - 1) + lo g_{3} (2 x) + 3

What is ln((e^{i0})/(4+3e^{i0)}) ?
The solution to ln((e^{i0})/(4+3e^{i0)}) is -ln(7)