What is ln((x^3sqrt(x-1))/(3x-12)) ?

The solution to ln((x^3sqrt(x-1))/(3x-12)) is 3ln(x)+ln(sqrt(x-1))-ln(3x-12)

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simplify ln((x^3sqrt(x-1))/(3x-12))

simplify

ln (\frac{x ^{3} x - 1}{3 x - 12})

3 ln (x) + ln (x - 1) - ln (3 x - 12)

Solution steps

ln (\frac{x ^{3} x - 1}{3 x - 12})

Apply log rule:

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

ln (\frac{x ^{3} x - 1}{3 x - 12}) = ln (x^{3} x - 1) - ln (3 x - 12)

= ln (x^{3} x - 1) - ln (3 x - 12)

Apply log rule:

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

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

= ln (x^{3}) + ln (x - 1) - ln (3 x - 12)

Apply log rule:

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

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

= 3 ln (x) + ln (x - 1) - ln (3 x - 12)

2 ln (\frac{5}{4})

lo g_{2} (\frac{ab}{4})

lo g_{5} (\frac{125}{x + 7})

ln (\frac{4 0 ^{2}}{2 0 ^{2}})

lo g_{10} (\frac{x ^{3} + y}{1000})

What is ln((x^3sqrt(x-1))/(3x-12)) ?
The solution to ln((x^3sqrt(x-1))/(3x-12)) is 3ln(x)+ln(sqrt(x-1))-ln(3x-12)