What is ln(x^2-2x+1)-ln(x^2+4) ?

The solution to ln(x^2-2x+1)-ln(x^2+4) is ln((x^2-2x+1)/(x^2+4))

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simplify ln(x^2-2x+1)-ln(x^2+4)

simplify

ln (x^{2} - 2 x + 1) - ln (x^{2} + 4)

ln (\frac{x ^{2} - 2 x + 1}{x ^{2} + 4})

Solution steps

ln (x^{2} - 2 x + 1) - ln (x^{2} + 4)

Apply log rule:

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

ln (x^{2} - 2 x + 1) - ln (x^{2} + 4) = ln (\frac{x ^{2} - 2 x + 1}{x ^{2} + 4})

= ln (\frac{x ^{2} - 2 x + 1}{x ^{2} + 4})

ln (5) + ln (8)

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

2 ln (x) - ln (1 - x)

2 (ln (8) - ln (4))

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

What is ln(x^2-2x+1)-ln(x^2+4) ?
The solution to ln(x^2-2x+1)-ln(x^2+4) is ln((x^2-2x+1)/(x^2+4))