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

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

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simplify ln| x/a+1|-ln| x/a-1|

simplify

ln \frac{x}{a} + 1 - ln \frac{x}{a} - 1

ln (\frac{∣ x + a ∣}{∣ x - a ∣})

Solution steps

ln \frac{x}{a} + 1 - ln \frac{x}{a} - 1

Apply log rule:

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

ln \frac{x}{a} + 1 - ln \frac{x}{a} - 1 = ln (\frac{\frac{x}{a} + 1}{\frac{x}{a} - 1})

= ln (\frac{\frac{x}{a} + 1}{\frac{x}{a} - 1})

Simplify

\frac{\frac{x}{a} + 1}{\frac{x}{a} - 1} : \frac{∣ x + a ∣}{∣ x - a ∣}

= ln (\frac{∣ x + a ∣}{∣ x - a ∣})

ln (\frac{1}{e ^{1.259}})

3 ln (3) + 2 ln (x)

lo g_{\frac{1}{2}} (\frac{1}{100})

ln (6) + 2 ln (5) - ln (2)

- lo g_{10} (1.25 \cdot 1 0^{- 3})

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