What is ln((x^2)/((2x-11)^2)) ?

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

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simplify ln((x^2)/((2x-11)^2))

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

= 2 ln (x) - 2 ln (2 x - 11)

ln (\frac{821.85}{1643}) \cdot 10

3 lo g_{3} (x) - 7 lo g_{3} (y)

1.75 ln ∣ y + 2 ∣ + 0.25 ln ∣ y - 3 ∣ + 2 ln ∣ y ∣

4 - \frac{1}{2} ln (2) - 1 + \frac{1}{2} ln (\frac{1}{2})

lo g_{8} (\frac{( x - 4 ) ( x - 1 ) ( 3 )}{5 x})

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