What is log_{8}((x^3cos(x))/(3x+1)) ?

The solution to log_{8}((x^3cos(x))/(3x+1)) is 3log_{8}(x)+log_{8}(cos(x))-log_{8}(3x+1)

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simplify log_{8}((x^3cos(x))/(3x+1))

simplify

lo g_{8} (\frac{x ^{3} cos ( x )}{3 x + 1})

3 lo g_{8} (x) + lo g_{8} (cos (x)) - lo g_{8} (3 x + 1)

Solution steps

lo g_{8} (\frac{x ^{3} cos ( x )}{3 x + 1})

Apply log rule:

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

lo g_{8} (\frac{x ^{3} cos ( x )}{3 x + 1}) = lo g_{8} (x^{3} cos (x)) - lo g_{8} (3 x + 1)

= lo g_{8} (x^{3} cos (x)) - lo g_{8} (3 x + 1)

Apply log rule:

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

lo g_{8} (x^{3} cos (x)) = lo g_{8} (x^{3}) + lo g_{8} (cos (x))

= lo g_{8} (x^{3}) + lo g_{8} (cos (x)) - lo g_{8} (3 x + 1)

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{8} (x^{3}) = 3 lo g_{8} (x)

= 3 lo g_{8} (x) + lo g_{8} (cos (x)) - lo g_{8} (3 x + 1)

ln (\frac{e ^{8}}{5})

lo g_{10}^{- 1} (\frac{0.1}{20}) - 1

ln (4 e^{3} x)

ln (3 x^{4} y^{6})

- 2 \cdot ln (\frac{0.2}{1.2})

What is log_{8}((x^3cos(x))/(3x+1)) ?
The solution to log_{8}((x^3cos(x))/(3x+1)) is 3log_{8}(x)+log_{8}(cos(x))-log_{8}(3x+1)