What is ln((x^2sqrt(x-1))/(3x-9)) ?

The solution to ln((x^2sqrt(x-1))/(3x-9)) is 2ln(x)+ln(sqrt(x-1))-ln(3x-9)

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simplify ln((x^2sqrt(x-1))/(3x-9))

simplify

ln (\frac{x ^{2} x - 1}{3 x - 9})

2 ln (x) + ln (x - 1) - ln (3 x - 9)

Solution steps

ln (\frac{x ^{2} x - 1}{3 x - 9})

Apply log rule:

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

ln (\frac{x ^{2} x - 1}{3 x - 9}) = ln (x^{2} x - 1) - ln (3 x - 9)

= ln (x^{2} x - 1) - ln (3 x - 9)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

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

= ln (x^{2}) + ln (x - 1) - ln (3 x - 9)

Apply log rule:

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

ln (x^{2}) = 2 ln (x)

= 2 ln (x) + ln (x - 1) - ln (3 x - 9)

ln (\frac{1}{60})

59 ln (\frac{1}{100})

lo g_{10} (\frac{1}{1 0 ^{521}})

ln (\frac{( 9 x + 16 y )}{( e ^{(1)} x ^{(2)} )})

What is ln((x^2sqrt(x-1))/(3x-9)) ?
The solution to ln((x^2sqrt(x-1))/(3x-9)) is 2ln(x)+ln(sqrt(x-1))-ln(3x-9)