What is 2ln(x^3+2)+2-2ln(-x^2+2x+2)-2 ?

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

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simplify 2ln(x^3+2)+2-2ln(-x^2+2x+2)-2

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

2 - 2 = 0

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

lo g_{5} (x + 3) + lo g_{5} (x - 3)

lo g_{12} (\frac{1}{2}) - lo g_{12} (8) + lo g_{12} (w)

lo g_{2} (3) + lo g_{2} (7)

lo g_{2} (10) + lo g_{2} (5)

lo g_{3} (2 x y)

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