What is log_{4}(((x^3*(x+3)))/((3x-2))) ?

The solution to log_{4}(((x^3*(x+3)))/((3x-2))) is 3log_{4}(x)+log_{4}(x+3)-log_{4}(3x-2)

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simplify log_{4}(((x^3*(x+3)))/((3x-2)))

simplify

lo g_{4} (\frac{( x ^{3} \cdot ( x + 3 ) )}{( 3 x - 2 )})

3 lo g_{4} (x) + lo g_{4} (x + 3) - lo g_{4} (3 x - 2)

Solution steps

lo g_{4} (\frac{x ^{3} ( x + 3 )}{3 x - 2})

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{4} (\frac{x ^{3} ( x + 3 )}{3 x - 2}) = lo g_{4} (x^{3} (x + 3)) - lo g_{4} (3 x - 2)

= lo g_{4} (x^{3} (x + 3)) - lo g_{4} (3 x - 2)

Simplify

lo g_{4} (x^{3} (x + 3)) : 3 lo g_{4} (x) + lo g_{4} (x + 3)

= 3 lo g_{4} (x) + lo g_{4} (x + 3) - lo g_{4} (3 x - 2)

(x + 3) (x^{2} - 6 x + 9)

\frac{( x ^{4} - 16 )}{( x ^{3} - 8 )}

(16 z)^{- 3} \cdot (4 z)^{3}

6 x - 3 y + 9

(x + 3) (x - 3) + 81

What is log_{4}(((x^3*(x+3)))/((3x-2))) ?
The solution to log_{4}(((x^3*(x+3)))/((3x-2))) is 3log_{4}(x)+log_{4}(x+3)-log_{4}(3x-2)