What is log_{e}(xy)-log_{e}(|x|) ?

The solution to log_{e}(xy)-log_{e}(|x|) is ln((xy)/(|x|))

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simplify log_{e}(xy)-log_{e}(|x|)

simplify

lo g_{e} (x y) - lo g_{e} (∣ x ∣)

ln (\frac{x y}{∣ x ∣})

Solution steps

lo g_{e} (x y) - lo g_{e} (∣ x ∣)

Apply log rule:

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

lo g_{e} (x y) - lo g_{e} (∣ x ∣) = lo g_{e} (\frac{x y}{∣ x ∣})

= lo g_{e} (\frac{x y}{∣ x ∣})

Apply log rule:

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

= ln (\frac{x y}{∣ x ∣})

9.26 + lo g_{10} (\frac{0.2}{0.23})

2 lo g_{10} (x) + lo g_{10} (a)

ln (4 e^{- 4})

3 ln (x + 2) - ln (x + 1)

3.85 + lo g_{10} (\frac{0.55}{0.85})

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