What is ln((1+0.5x+0.5x^2)/(2+1/3)) ?

The solution to ln((1+0.5x+0.5x^2)/(2+1/3)) is ln(1+0.5x+0.5x^2)-ln(7/3)

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simplify ln((1+0.5x+0.5x^2)/(2+1/3))

simplify

ln (\frac{1 + 0.5 x + 0.5 x ^{2}}{2 + \frac{1}{3}})

ln (1 + 0.5 x + 0.5 x^{2}) - ln (\frac{7}{3})

Solution steps

ln (\frac{1 + 0.5 x + 0.5 x ^{2}}{2 + \frac{1}{3}})

Apply log rule:

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

ln (\frac{1 + 0.5 x + 0.5 x ^{2}}{2 + \frac{1}{3}}) = ln (1 + 0.5 x + 0.5 x^{2}) - ln (2 + \frac{1}{3})

= ln (0.5 x^{2} + 0.5 x + 1) - ln (\frac{1}{3} + 2)

Join

2 + \frac{1}{3} : \frac{7}{3}

= ln (0.5 x^{2} + 0.5 x + 1) - ln (\frac{7}{3})

ln (y^{3}) + \frac{1}{3} ln (x^{9} y^{12}) - 7 ln (y)

ln (2 \cdot 4)

ln (\frac{1}{3}) - ln (\frac{1}{2})

ln (\frac{e ^{3 x} ( x + 1 )}{2 x ^{12}})

3 \cdot lo g_{10} (x - 3) - 4.5 lo g_{10} (x - 2)

What is ln((1+0.5x+0.5x^2)/(2+1/3)) ?
The solution to ln((1+0.5x+0.5x^2)/(2+1/3)) is ln(1+0.5x+0.5x^2)-ln(7/3)