What is ln((1+ax+bx^2}{2+\frac{2b)/3}) ?

The solution to ln((1+ax+bx^2}{2+\frac{2b)/3}) is ln(1+ax+bx^2)-ln(2+(2b)/3)

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simplify ln((1+ax+bx^2}{2+\frac{2b)/3})

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

lo g_{10} (\frac{3 + i}{2})

\frac{1}{3} ln (\frac{3 x + 16 + 9 x ^{2}}{4}) + C

ln ((0.5 + \frac{0.044315}{2}) (1.05))

3 (- \frac{1}{6} ln ∣ x + 2 ∣ + \frac{1}{6} ln ∣ x - 4 ∣) + C

lo g_{3} ((2 x)^{2})

What is ln((1+ax+bx^2}{2+\frac{2b)/3}) ?
The solution to ln((1+ax+bx^2}{2+\frac{2b)/3}) is ln(1+ax+bx^2)-ln(2+(2b)/3)