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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

lo g_{10} (7 x^{3} y)

ln (\frac{x}{2 y})

ln ∣ x ∣ + ln cos (\frac{y}{x})

\frac{1}{6} ln x^{2} + 9 + \frac{1}{6} ln \frac{x ^{2}}{9} + 1

ln (\frac{x ^{4}}{y ^{5}})

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