What is ln(((x^2-1))/(x^9)) ?

The solution to ln(((x^2-1))/(x^9)) is ln(x^2-1)-9ln(x)

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simplify ln(((x^2-1))/(x^9))

simplify

ln (\frac{( x ^{2} - 1 )}{x ^{9}})

ln (x^{2} - 1) - 9 ln (x)

Solution steps

ln (\frac{( x ^{2} - 1 )}{x ^{9}})

Apply log rule:

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

ln (\frac{( x ^{2} - 1 )}{x ^{9}}) = ln ((x^{2} - 1)) - ln (x^{9})

= ln (x^{2} - 1) - ln (x^{9})

Apply log rule:

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

ln (x^{9}) = 9 ln (x)

= ln (x^{2} - 1) - 9 ln (x)

7 lo g_{7} (5 x)

lo g_{10} (\frac{2 a ^{2}}{b})

lo g_{b} (\frac{3.839}{0.32})

lo g_{3} (\frac{z}{9})

lo g_{10} (\frac{x ^{9} y ^{5}}{z ^{3}})

What is ln(((x^2-1))/(x^9)) ?
The solution to ln(((x^2-1))/(x^9)) is ln(x^2-1)-9ln(x)