What is ln(2(sqrt(3)+i)^3) ?

The solution to ln(2(sqrt(3)+i)^3) is ln(2)+3ln(sqrt(3)+i)

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simplify ln(2(sqrt(3)+i)^3)

simplify

ln (2 (3 + i)^{3})

ln (2) + 3 ln (3 + i)

Solution steps

ln (2 (3 + i)^{3})

Apply log rule:

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

ln (2 (3 + i)^{3}) = ln (2) + ln ((3 + i)^{3})

= ln (2) + ln ((3 + i)^{3})

Apply log rule:

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

ln ((3 + i)^{3}) = 3 ln (3 + i)

= ln (2) + 3 ln (3 + i)

\frac{12}{5} \cdot lo g_{2} (5)

ln (5) - ln (2) - \frac{3}{10}

- ln (y) + ln (x)

ln (x^{3} + 9) - ln (3 n^{3} + 13 n)

ln (2 x yz)

What is ln(2(sqrt(3)+i)^3) ?
The solution to ln(2(sqrt(3)+i)^3) is ln(2)+3ln(sqrt(3)+i)