What is ln(e^{i0})-ln(3e^{i0}+4) ?

The solution to ln(e^{i0})-ln(3e^{i0}+4) is -ln(7)

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simplify ln(e^{i0})-ln(3e^{i0}+4)

simplify

ln (e^{i 0}) - ln (3 e^{i 0} + 4)

- ln (7)

Decimal Notation

- 1.94591 \dots

Solution steps

ln (e^{i 0}) - ln (3 e^{i 0} + 4)

Apply log rule:

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

ln (e^{0 i}) - ln (3 e^{0 i} + 4) = ln (\frac{e ^{0 i}}{3 e ^{0 i} + 4})

= ln (\frac{e ^{i 0}}{3 e ^{i 0} + 4})

\frac{e ^{i 0}}{3 e ^{i 0} + 4} = \frac{1}{7}

= ln (\frac{1}{7})

Apply log rule:

lo g_{a} (\frac{1}{x}) = - lo g_{a} (x)

= - ln (7)

12 ln (x) - 14 ln (\frac{1}{y}) - 13 ln (x y)

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5 lo g_{10} (x) - (3 lo g_{10} (y) + lo g_{10} (z))

What is ln(e^{i0})-ln(3e^{i0}+4) ?
The solution to ln(e^{i0})-ln(3e^{i0}+4) is -ln(7)