What is ln((-sin(4x)4)/(cos(4x))) ?

The solution to ln((-sin(4x)4)/(cos(4x))) is ln(sin(4x))+2ln(2)-ln(cos(4x))

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simplify ln((-sin(4x)4)/(cos(4x)))

simplify

ln (\frac{- sin ( 4 x ) 4}{cos ( 4 x )})

ln (sin (4 x)) + 2 ln (2) - ln (cos (4 x))

Solution steps

ln (\frac{- sin ( 4 x ) \cdot 4}{cos ( 4 x )})

Apply log rule:

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

ln (\frac{- sin ( 4 x ) \cdot 4}{cos ( 4 x )}) = ln (- sin (4 x) \cdot 4) - ln (cos (4 x))

= ln (- 4 sin (4 x)) - ln (cos (4 x))

Apply log rule:

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

ln (- sin (4 x) \cdot 4) = ln (sin (4 x)) + ln (4)

= ln (sin (4 x)) + ln (4) - ln (cos (4 x))

ln (4) = 2 ln (2)

= ln (sin (4 x)) + 2 ln (2) - ln (cos (4 x))

ln (\frac{1.5}{1})

2 lo g_{a} (C) + 3 lo g_{a} (P) + 1

ln ∣ p ∣ - ln ∣ 1 - p ∣

\frac{2}{5} lo g_{a} (x) - \frac{1}{3} lo g_{a} (y)

What is ln((-sin(4x)4)/(cos(4x))) ?
The solution to ln((-sin(4x)4)/(cos(4x))) is ln(sin(4x))+2ln(2)-ln(cos(4x))