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

The solution to ln((e^{ipi})/(4+3e^{ipi)}) is ipi

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

simplify

ln (\frac{e ^{iπ}}{4 + 3 e ^{iπ}})

iπ

Solution steps

ln (\frac{e ^{iπ}}{4 + 3 e ^{iπ}})

Apply log rule:

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

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

= ln (e^{iπ}) - ln (3 e^{iπ} + 4)

Apply log rule:

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

ln (e^{iπ}) = iπ ln (e)

= iπ ln (e) - ln (4 + 3 e^{iπ})

iπ ln (e) = iπ

ln (4 + 3 e^{iπ}) = 0

= iπ - 0

iπ - 0 = iπ

= iπ

lo g_{8} (8 x)

lo g_{3} (4) + lo g_{3} (6)

lo g_{4} (\frac{1}{16} m n^{2})

lo g_{q} (4 y)

ln (\frac{33.87}{29.76})

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