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

The solution to log_{4}((x^2-2x-3)/(x^2-3x)) is log_{4}(x+1)-log_{4}(x)

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

simplify

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

lo g_{4} (x + 1) - lo g_{4} (x)

Solution steps

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

Simplify

\frac{x ^{2} - 2 x - 3}{x ^{2} - 3 x} : \frac{x + 1}{x}

= lo g_{4} (\frac{x + 1}{x})

Apply log rule:

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

lo g_{4} (\frac{x + 1}{x}) = lo g_{4} (x + 1) - lo g_{4} (x)

= lo g_{4} (x + 1) - lo g_{4} (x)

ln (x^{8} y^{3} z)

ln (y \frac{y}{5 - y})

lo g_{6} (x \cdot y \cdot z^{5})

π (3 \cdot ln (3) - 2 \cdot ln (2) + 1)

8 lo g_{6} (u) + 9 lo g_{6} (v)

What is log_{4}((x^2-2x-3)/(x^2-3x)) ?
The solution to log_{4}((x^2-2x-3)/(x^2-3x)) is log_{4}(x+1)-log_{4}(x)