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Popular >

simplify ln(8e^{ipi})

Solution

simplify

ln (8 e^{iπ})

Solution

3 ln (2) + iπ

Solution steps

ln (8 e^{iπ})

Apply log rule:

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

ln (8 e^{iπ}) = ln (8) + ln (e^{iπ})

= ln (8) + ln (e^{iπ})

Apply log rule:

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

ln (e^{iπ}) = iπ ln (e)

= ln (8) + iπ ln (e)

iπ ln (e) = iπ

= ln (8) + iπ

ln (8) = 3 ln (2)

= 3 ln (2) + iπ

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Frequently Asked Questions (FAQ)

What is ln(8e^{ipi}) ?
The solution to ln(8e^{ipi}) is 3ln(2)+ipi