What is log_{b}((x^2-1)/(x^2-4)) ?

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

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simplify log_{b}((x^2-1)/(x^2-4))

simplify

lo g_{b} (\frac{x ^{2} - 1}{x ^{2} - 4})

lo g_{b} (x^{2} - 1) - lo g_{b} (x^{2} - 4)

Solution steps

lo g_{b} (\frac{x ^{2} - 1}{x ^{2} - 4})

Apply log rule:

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

lo g_{b} (\frac{x ^{2} - 1}{x ^{2} - 4}) = lo g_{b} (x^{2} - 1) - lo g_{b} (x^{2} - 4)

= lo g_{b} (x^{2} - 1) - lo g_{b} (x^{2} - 4)

lo g_{10} (\frac{4 x ^{3}}{y ^{2} ( x - 1 ) ^{5}})

10 ln (3 x) - [ln (3 x)]^{2}

ln (\frac{1}{θ} \cdot [1 - \frac{1}{θ}]^{x - 1})

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

5 ln (x) - \frac{1}{4} ln (y)

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