What is ln((sqrt(x^2-4))/(x^2-7x+12)) ?

The solution to ln((sqrt(x^2-4))/(x^2-7x+12)) is ln(sqrt(x^2-4))-ln(x^2-7x+12)

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simplify ln((sqrt(x^2-4))/(x^2-7x+12))

simplify

ln (\frac{x ^{2} - 4}{x ^{2} - 7 x + 12})

ln (x^{2} - 4) - ln (x^{2} - 7 x + 12)

Solution steps

ln (\frac{x ^{2} - 4}{x ^{2} - 7 x + 12})

Apply log rule:

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

ln (\frac{x ^{2} - 4}{x ^{2} - 7 x + 12}) = ln (x^{2} - 4) - ln (x^{2} - 7 x + 12)

= ln (x^{2} - 4) - ln (x^{2} - 7 x + 12)

2 ln (4) + 6 ln (x) - 3 ln (2)

ln (a^{4} b^{7})

ln (\frac{19}{39})

ln (A) + ln (B)

8 lo g_{2} (a) + 2 lo g_{2} (b)

What is ln((sqrt(x^2-4))/(x^2-7x+12)) ?
The solution to ln((sqrt(x^2-4))/(x^2-7x+12)) is ln(sqrt(x^2-4))-ln(x^2-7x+12)