What is ln((3z+2i)/(4z-5i)) ?

The solution to ln((3z+2i)/(4z-5i)) is ln(3z+2i)-ln(4z-5i)

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simplify ln((3z+2i)/(4z-5i))

simplify

ln (\frac{3 z + 2 i}{4 z - 5 i})

ln (3 z + 2 i) - ln (4 z - 5 i)

Solution steps

ln (\frac{3 z + 2 i}{4 z - 5 i})

Apply log rule:

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

ln (\frac{3 z + 2 i}{4 z - 5 i}) = ln (3 z + 2 i) - ln (4 z - 5 i)

= ln (3 z + 2 i) - ln (4 z - 5 i)

ln (e^{x} + 1) + ln (e^{- x} + 1)

ln (\frac{77 \cdot 914555 - 77}{914555 - 77})

ln (x^{2} + 4) + ln (x^{2} + x)

ln (15) - 2 (ln (4) + ln (32))

ln (\frac{5}{4}) \cdot 25

What is ln((3z+2i)/(4z-5i)) ?
The solution to ln((3z+2i)/(4z-5i)) is ln(3z+2i)-ln(4z-5i)