What is ln(4e^{(pii)/2}) ?

The solution to ln(4e^{(pii)/2}) is 2ln(2)+(pii)/2

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simplify ln(4e^{(pii)/2})

simplify

ln (4 e^{\frac{πi}{2}})

2 ln (2) + \frac{πi}{2}

Solution steps

ln (4 e^{\frac{πi}{2}})

Apply log rule:

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

ln (4 e^{\frac{πi}{2}}) = ln (4) + ln (e^{\frac{πi}{2}})

= ln (4) + ln (e^{\frac{πi}{2}})

Apply log rule:

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

ln (e^{\frac{πi}{2}}) = \frac{πi}{2} ln (e)

= ln (4) + \frac{πi}{2} ln (e)

\frac{πi}{2} ln (e) = \frac{πi}{2}

= ln (4) + \frac{πi}{2}

ln (4) = 2 ln (2)

= 2 ln (2) + \frac{πi}{2}

ln (\frac{0.7285}{0.7285 - 0.1314})

ln (\frac{n ^{2} + 2}{3 n ^{2} + 5})

25.12 ln (\frac{253.67}{365}) + (8.314 \cdot ln (3))

ln (2 y^{2}) - ln (y^{2})

ln (\frac{6.94 \cdot 1 0 ^{- 6}}{804.11})