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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

ln (\frac{3 \cdot x ^{3} + 2 \cdot π}{9 \cdot x + c})

- ln ∣ p ∣ + ln ∣ p - 3 ∣

ln (x^{3} \cdot y z)

ln ∣ x - 2 ∣ - ln ∣ x - 1 ∣

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

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