What is log_{5}((\sqrt[3]{x^2+1})/(x^2-1)) ?

The solution to log_{5}((\sqrt[3]{x^2+1})/(x^2-1)) is log_{5}(\sqrt[3]{x^2+1})-log_{5}(x^2-1)

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simplify log_{5}((\sqrt[3]{x^2+1})/(x^2-1))

simplify

Solution steps

Apply log rule:

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

lo g_{4} (x^{2} - 25) - 6 lo g_{4} (x + 5)

lo g_{a} (\frac{x ^{2}}{y z ^{3}})

\frac{1}{2} (lo g_{5} (x - 8) - lo g_{5} (x))

lo g_{4} (\frac{x ^{2}}{5})

lo g_{10} (1 x)

What is log_{5}((\sqrt[3]{x^2+1})/(x^2-1)) ?
The solution to log_{5}((\sqrt[3]{x^2+1})/(x^2-1)) is log_{5}(\sqrt[3]{x^2+1})-log_{5}(x^2-1)