What is ln((x^2-4x+3)/(x^2-5x+6)) ?

The solution to ln((x^2-4x+3)/(x^2-5x+6)) is ln(x^2-4x+3)-ln(x^2-5x+6)

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simplify ln((x^2-4x+3)/(x^2-5x+6))

simplify

ln (\frac{x ^{2} - 4 x + 3}{x ^{2} - 5 x + 6})

ln (x^{2} - 4 x + 3) - ln (x^{2} - 5 x + 6)

Solution steps

ln (\frac{x ^{2} - 4 x + 3}{x ^{2} - 5 x + 6})

Apply log rule:

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

ln (\frac{x ^{2} - 4 x + 3}{x ^{2} - 5 x + 6}) = ln (x^{2} - 4 x + 3) - ln (x^{2} - 5 x + 6)

= ln (x^{2} - 4 x + 3) - ln (x^{2} - 5 x + 6)

- \frac{9}{14} \cdot lo g_{2} (\frac{9}{14}) - \frac{5}{14} \cdot lo g_{2} (\frac{5}{14})

lo g_{10} (\frac{x y ^{4}}{z ^{5}})

lo g_{5} (A) + lo g_{5} (B)

What is ln((x^2-4x+3)/(x^2-5x+6)) ?
The solution to ln((x^2-4x+3)/(x^2-5x+6)) is ln(x^2-4x+3)-ln(x^2-5x+6)