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

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

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

simplify

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

ln (sin (x)) + ln (cos^{4} (x)) - 2 ln (2)

Solution steps

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

Apply log rule:

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

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

= ln (sin (x) cos^{4} (x)) - ln (4)

Apply log rule:

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

ln (sin (x) cos^{4} (x)) = ln (sin (x)) + ln (cos^{4} (x))

= ln (sin (x)) + ln (cos^{4} (x)) - ln (4)

ln (4) = 2 ln (2)

= ln (sin (x)) + ln (cos^{4} (x)) - 2 ln (2)

ln (\frac{90}{70})

- lo g_{10} (3.16 \cdot 1 0^{- 12})

ln (2 x) 4

- lo g_{10} (1.7 \cdot 1 0^{- 12})

ln ∣ x ∣ + 2 ln x^{2} + 4 + C

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