What is 11ln(x-2)-3ln(x) ?

The solution to 11ln(x-2)-3ln(x) is ln(((x-2)^{11})/(x^3))

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simplify 11ln(x-2)-3ln(x)

simplify

11 ln (x - 2) - 3 ln (x)

ln (\frac{( x - 2 ) ^{11}}{x ^{3}})

Solution steps

11 ln (x - 2) - 3 ln (x)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

11 ln (x - 2) = ln ((x - 2)^{11})

= ln ((x - 2)^{11}) - 3 ln (x)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

= ln ((x - 2)^{11}) - ln (x^{3})

Apply log rule:

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

ln ((x - 2)^{11}) - ln (x^{3}) = ln (\frac{( x - 2 ) ^{11}}{x ^{3}})

= ln (\frac{( x - 2 ) ^{11}}{x ^{3}})

ln (e (x + 7))

ln (\frac{s}{s - 3})

4 ln (x) - 3 ln (y)

4 lo g_{10} (9) - 4 lo g_{10} (x)

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

What is 11ln(x-2)-3ln(x) ?
The solution to 11ln(x-2)-3ln(x) is ln(((x-2)^{11})/(x^3))