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

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

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

expand

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)

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

lo g_{n} (\frac{4}{n})

\frac{2}{3} lo g_{10} (7)

lo g_{b} (\frac{p ^{3} q ^{6}}{m ^{5} b ^{7}})

7 lo g_{b} (x) + 5 lo g_{b} (z)

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