What is 11ln(x-4)-2ln(x) ?

The solution to 11ln(x-4)-2ln(x) is ln(((x-4)^{11})/(x^2))

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simplify 11ln(x-4)-2ln(x)

simplify

11 ln (x - 4) - 2 ln (x)

ln (\frac{( x - 4 ) ^{11}}{x ^{2}})

Solution steps

11 ln (x - 4) - 2 ln (x)

Apply log rule:

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

11 ln (x - 4) = ln ((x - 4)^{11})

= ln ((x - 4)^{11}) - 2 ln (x)

Apply log rule:

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

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

= ln ((x - 4)^{11}) - ln (x^{2})

Apply log rule:

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

ln ((x - 4)^{11}) - ln (x^{2}) = ln (\frac{( x - 4 ) ^{11}}{x ^{2}})

= ln (\frac{( x - 4 ) ^{11}}{x ^{2}})

- (\frac{2}{3} \cdot lo g_{2} (\frac{2}{3}) + \frac{1}{3} \cdot lo g_{2} (\frac{1}{3}))

lo g_{5} (x) - lo g_{5} (2)

ln ((cos (x))^{\frac{1}{x ^{2}}})

lo g_{10} (100 x^{3})

ln (18) - ln (9)

What is 11ln(x-4)-2ln(x) ?
The solution to 11ln(x-4)-2ln(x) is ln(((x-4)^{11})/(x^2))