What is log_{3}(sin(x)cos(x))-log_{3}(3^xe^x) ?

The solution to log_{3}(sin(x)cos(x))-log_{3}(3^xe^x) is log_{3}((sin(x)cos(x))/(3^xe^x))

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simplify log_{3}(sin(x)cos(x))-log_{3}(3^xe^x)

simplify

lo g_{3} (sin (x) cos (x)) - lo g_{3} (3^{x} e^{x})

lo g_{3} (\frac{sin ( x ) cos ( x )}{3 ^{x} e ^{x}})

Solution steps

lo g_{3} (sin (x) cos (x)) - lo g_{3} (3^{x} e^{x})

Apply log rule:

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

lo g_{3} (sin (x) cos (x)) - lo g_{3} (3^{x} e^{x}) = lo g_{3} (\frac{sin ( x ) cos ( x )}{3 ^{x} e ^{x}})

= lo g_{3} (\frac{sin ( x ) cos ( x )}{3 ^{x} e ^{x}})

\frac{1}{- ( 0.005 )} [0.8 ln (\frac{1}{8}) + 0.2 ln (\frac{9}{2})]

ln (e^{x} sin (2 x))

\frac{ln ( \frac{A}{b} )}{2 ln ( 10 )}

\frac{1}{2} ln (2 x + 5) - \frac{1}{3} ln (x + 8) + ln (C)

- lo g_{10} (7.83 \cdot 1 0^{- 8})

What is log_{3}(sin(x)cos(x))-log_{3}(3^xe^x) ?
The solution to log_{3}(sin(x)cos(x))-log_{3}(3^xe^x) is log_{3}((sin(x)cos(x))/(3^xe^x))