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

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

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

simplify

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

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

Solution steps

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

Simplify

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

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

Apply log rule:

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

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

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

\frac{3}{2} ln (a) + \frac{1}{2} ln (b) - 1

2 lo g_{b} (w) + 4 (lo g_{b} (x) - 5 lo g_{b} (z))

lo g_{6} (\frac{x ^{3}}{y ^{6}})

lo g_{2} (\frac{15}{y})

lo g_{2} (x) + lo g_{2} (x + 15) + lo g_{2} (16)

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