What is ln|x|+ln|x-1|+ln|x+1| ?

The solution to ln|x|+ln|x-1|+ln|x+1| is ln(|x||x-1||x+1|)

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simplify ln|x|+ln|x-1|+ln|x+1|

simplify

ln ∣ x ∣ + ln ∣ x - 1 ∣ + ln ∣ x + 1 ∣

ln (∣ x ∣ ∣ x - 1 ∣ ∣ x + 1 ∣)

Solution steps

ln ∣ x ∣ + ln ∣ x - 1 ∣ + ln ∣ x + 1 ∣

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

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

= ln (∣ x ∣ ∣ x - 1 ∣) + ln ∣ x + 1 ∣

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

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

= ln (∣ x ∣ ∣ x - 1 ∣ ∣ x + 1 ∣)

ln ∣ b ∣ ln (\frac{b}{a}) + \frac{- ln ( ∣ b ∣ ^{2} ) + ln ( ∣ a ∣ ^{2} )}{2}

0 \cdot lo g_{10} (0.69) + (1 - 0) \cdot lo g_{10} (1 - 0.69)

lo g_{5} (\frac{1}{20})

- lo g_{10} (3.2 \cdot 1 0^{- 6})

\frac{1}{0.00499} ln (\frac{400 - 15}{75 - 15})

What is ln|x|+ln|x-1|+ln|x+1| ?
The solution to ln|x|+ln|x-1|+ln|x+1| is ln(|x||x-1||x+1|)