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)

ln (x) + ln (\frac{y}{x})

lo g_{4} (8) + lo g_{4} (x)

ln (3 e^{5})

lo g_{4} (\frac{y}{( x + 1 ) ^{2}})

5 ln (x) + 2 ln (y) - 3 ln (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)