What is log_{10}((x^2-1)/(x^3)) ?

The solution to log_{10}((x^2-1)/(x^3)) is log_{10}(x^2-1)-3log_{10}(x)

Popular >

simplify log_{10}((x^2-1)/(x^3))

simplify

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

lo g_{10} (x^{2} - 1) - 3 lo g_{10} (x)

Solution steps

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

Apply log rule:

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

lo g_{10} (\frac{x ^{2} - 1}{x ^{3}}) = lo g_{10} (x^{2} - 1) - lo g_{10} (x^{3})

= lo g_{10} (x^{2} - 1) - lo g_{10} (x^{3})

Simplify

lo g_{10} (x^{3}) : 3 lo g_{10} (x)

= lo g_{10} (x^{2} - 1) - 3 lo g_{10} (x)

ln^{2} (4 x)

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

(- \frac{6}{10}) lo g_{2} (\frac{6}{10}) - (\frac{4}{10}) lo g_{2} (\frac{4}{10})

- (\frac{2}{6}) lo g_{2} (\frac{2}{6}) - (\frac{4}{6}) lo g_{2} (\frac{4}{6})

lo g_{10} (x) - 5 lo g_{10} (y) + 8 lo g_{10} (z)

What is log_{10}((x^2-1)/(x^3)) ?
The solution to log_{10}((x^2-1)/(x^3)) is log_{10}(x^2-1)-3log_{10}(x)