What is ln(\mid cos(θ)2(ln|1+cos(2θ)|-ln(2))) ?

The solution to ln(\mid cos(θ)2(ln|1+cos(2θ)|-ln(2))) is ln(\mid cos(θ)*2ln(cos^2(θ)))

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simplify ln(\mid cos(θ)2(ln|1+cos(2θ)|-ln(2)))

simplify

ln (∣ cos (θ) 2 (ln ∣ 1 + cos (2 θ) ∣ - ln (2)))

ln (∣ cos (θ) \cdot 2 ln (cos^{2} (θ)))

Solution steps

ln (∣ cos (θ) \cdot 2 (ln ∣ 1 + cos (2 θ) ∣ - ln (2)))

Apply log rule:

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

ln ∣ 1 + cos (2 θ) ∣ - ln (2) = ln (\frac{∣ cos ( 2 θ ) + 1 ∣}{2})

= ln (2 ∣ cos (θ) ln (\frac{∣ cos ( 2 θ ) + 1 ∣}{2}))

Simplify

\frac{∣ 1 + cos ( 2 θ ) ∣}{2} : cos^{2} (θ)

= ln (∣ cos (θ) \cdot 2 ln (cos^{2} (θ)))

ln (e^{3 x} \cdot sin (2 x))

ln (- 2 \cdot e^{- x})

ln (x^{3} + 8) - ln (6 x^{3} + 17 x)

\frac{1}{3} ln (\frac{47}{73})

ln (2^{3} + 4) - ln (8 \cdot (2)^{3} + 15 (2))

What is ln(\mid cos(θ)2(ln|1+cos(2θ)|-ln(2))) ?
The solution to ln(\mid cos(θ)2(ln|1+cos(2θ)|-ln(2))) is ln(\mid cos(θ)*2ln(cos^2(θ)))