What is ln(4/(sin(3x-3))) ?

The solution to ln(4/(sin(3x-3))) is 2ln(2)-ln(sin(3x-3))

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simplify ln(4/(sin(3x-3)))

simplify

ln (\frac{4}{sin ( 3 x - 3 )})

2 ln (2) - ln (sin (3 x - 3))

Solution steps

ln (\frac{4}{sin ( 3 x - 3 )})

Apply log rule:

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

ln (\frac{4}{sin ( 3 x - 3 )}) = ln (4) - ln (sin (3 x - 3))

= ln (4) - ln (sin (3 x - 3))

ln (4) = 2 ln (2)

= 2 ln (2) - ln (sin (3 x - 3))

ln (10) - ln (40)

lo g_{10} (x^{3} y)

ln (x) + ln (25)

ln (y + 1) - ln (y - 1)

- lo g_{10} (4.5 \cdot 1 0^{- 11})

What is ln(4/(sin(3x-3))) ?
The solution to ln(4/(sin(3x-3))) is 2ln(2)-ln(sin(3x-3))