What is log_{e}((|x+1|-1)/(|x-3|+1)) ?

The solution to log_{e}((|x+1|-1)/(|x-3|+1)) is ln(|x+1|-1)-ln(|x-3|+1)

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simplify log_{e}((|x+1|-1)/(|x-3|+1))

simplify

lo g_{e} (\frac{∣ x + 1 ∣ - 1}{∣ x - 3 ∣ + 1})

ln (∣ x + 1 ∣ - 1) - ln (∣ x - 3 ∣ + 1)

Solution steps

lo g_{e} (\frac{∣ x + 1 ∣ - 1}{∣ x - 3 ∣ + 1})

Apply log rule:

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

lo g_{e} (\frac{∣ x + 1 ∣ - 1}{∣ x - 3 ∣ + 1}) = lo g_{e} (∣ x + 1 ∣ - 1) - lo g_{e} (∣ x - 3 ∣ + 1)

= lo g_{e} (∣ x + 1 ∣ - 1) - lo g_{e} (∣ x - 3 ∣ + 1)

Apply log rule:

lo g_{e} (x) = ln (x)

= ln (∣ x + 1 ∣ - 1) - lo g_{e} (∣ x - 3 ∣ + 1)

Apply log rule:

lo g_{e} (x) = ln (x)

= ln (∣ x + 1 ∣ - 1) - ln (∣ x - 3 ∣ + 1)

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

ln (\frac{13}{15})

lo g_{2} (\frac{4}{x + 9})

- 8 lo g_{6} (- 4 n) + 16

lo g_{10} ((5 x - 3)^{2}) + lo g_{10} ((2 x + 3)^{2}) 0

What is log_{e}((|x+1|-1)/(|x-3|+1)) ?
The solution to log_{e}((|x+1|-1)/(|x-3|+1)) is ln(|x+1|-1)-ln(|x-3|+1)