What is simplify-1/2 ln|u|+1/2 ln|u-2| ?

The solution to simplify-1/2 ln|u|+1/2 ln|u-2| is ln(sqrt((|u-2|)/(|u|)))

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simplify-1/2 ln|u|+1/2 ln|u-2|

simplify

- \frac{1}{2} ln ∣ u ∣ + \frac{1}{2} ln ∣ u - 2 ∣

ln (\frac{∣ u - 2 ∣}{∣ u ∣})

Solution steps

- \frac{1}{2} ln ∣ u ∣ + \frac{1}{2} ln ∣ u - 2 ∣

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{1}{2} ln ∣ u ∣ = ln (∣ u ∣^{\frac{1}{2}})

= - ln (∣ u ∣^{\frac{1}{2}}) + \frac{1}{2} ln ∣ u - 2 ∣

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{1}{2} ln ∣ u - 2 ∣ = ln (∣ u - 2 ∣^{\frac{1}{2}})

= - ln (∣ u ∣^{\frac{1}{2}}) + ln (∣ u - 2 ∣^{\frac{1}{2}})

Apply log rule:

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

ln (∣ u - 2 ∣^{\frac{1}{2}}) - ln (∣ u ∣^{\frac{1}{2}}) = ln (\frac{∣ u - 2 ∣ ^{\frac{1}{2}}}{∣ u ∣ ^{\frac{1}{2}}})

= ln (\frac{∣ u - 2 ∣ ^{\frac{1}{2}}}{∣ u ∣ ^{\frac{1}{2}}})

Combine same powers :

= ln (\frac{∣ u - 2 ∣}{∣ u ∣})

lo g_{m} (\frac{x ^{3}}{y ^{2}})

lo g_{π} (\frac{π ^{3} x ^{4} y ^{5} z}{( x - 1 ) ^{2} z})

ln (\frac{s}{s + 1})

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

What is simplify-1/2 ln|u|+1/2 ln|u-2| ?
The solution to simplify-1/2 ln|u|+1/2 ln|u-2| is ln(sqrt((|u-2|)/(|u|)))