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Popular >

simplify ln((x^2-1)/(x^3))

Solution

simplify

ln (\frac{x ^{2} - 1}{x ^{3}})

Solution

ln (x^{2} - 1) - 3 ln (x)

Solution steps

ln (\frac{x ^{2} - 1}{x ^{3}})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{x ^{2} - 1}{x ^{3}}) = ln (x^{2} - 1) - ln (x^{3})

= ln (x^{2} - 1) - ln (x^{3})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (x^{3}) = 3 ln (x)

= ln (x^{2} - 1) - 3 ln (x)

Popular Examples

simplify 3log_{b}(x)+2log_{b}(y)-1/2 log_{b}(z)simplify

3 lo g_{b} (x) + 2 lo g_{b} (y) - \frac{1}{2} lo g_{b} (z)

simplify log_{10}((x^3y)/z)simplify

lo g_{10} (\frac{x ^{3} y}{z})

simplify 4log_{10}(x/5)simplify

4 lo g_{10} (\frac{x}{5})

simplify-log_{10}(6.5*10^{-5})simplify

- lo g_{10} (6.5 \cdot 1 0^{- 5})

simplify log_{3}(x)+log_{3}(x+8)simplify

lo g_{3} (x) + lo g_{3} (x + 8)

Frequently Asked Questions (FAQ)

What is ln((x^2-1)/(x^3)) ?
The solution to ln((x^2-1)/(x^3)) is ln(x^2-1)-3ln(x)