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

The solution to ln(e^{ipi})-ln(3e^{ipi}+4) is ln(-1)

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

simplify

ln (e^{iπ}) - ln (3 e^{iπ} + 4)

ln (- 1)

Solution steps

ln (e^{iπ}) - ln (3 e^{iπ} + 4)

Apply log rule:

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

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

= ln (\frac{e ^{iπ}}{3 e ^{iπ} + 4})

\frac{e ^{iπ}}{3 e ^{iπ} + 4} = - 1

= ln (- 1)

8 lo g_{10} (x) - lo g_{10} (\frac{1}{x}) - lo g_{10} (y)

lo g_{10} (x^{2} y^{3} z^{4})

lo g_{10} (x) + 2 lo g_{10} (y) - 3 lo g_{10} (a)

ln (2 x) - ln (x)

lo g_{3} (\frac{x ^{4}}{x - 4})

What is ln(e^{ipi})-ln(3e^{ipi}+4) ?
The solution to ln(e^{ipi})-ln(3e^{ipi}+4) is ln(-1)