What is ln((|a|)/2)+ln| a/2+h| ?

The solution to ln((|a|)/2)+ln| a/2+h| is ln((|a||a+2h|)/4)

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simplify ln((|a|)/2)+ln| a/2+h|

simplify

ln (\frac{∣ a ∣}{2}) + ln \frac{a}{2} + h

ln (\frac{∣ a ∣ ∣ a + 2 h ∣}{4})

Solution steps

ln (\frac{∣ a ∣}{2}) + ln \frac{a}{2} + h

Apply log rule:

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

ln (\frac{∣ a ∣}{2}) + ln \frac{a}{2} + h = ln (\frac{∣ a ∣}{2} h + \frac{a}{2})

= ln (\frac{∣ a ∣}{2} h + \frac{a}{2})

Simplify

\frac{∣ a ∣}{2} \frac{a}{2} + h : \frac{∣ a ∣ ∣ a + 2 h ∣}{4}

= ln (\frac{∣ a ∣ ∣ a + 2 h ∣}{4})

4 ln (x) + \frac{1}{3} ln (x - 3) - 4 ln (2 x - 1) - 2022

\frac{1}{2} ln (\frac{1}{2})

ln (4) + 6 ln (x) - 2 ln (y)

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

ln (\frac{3 x ^{2}}{7 y})

What is ln((|a|)/2)+ln| a/2+h| ?
The solution to ln((|a|)/2)+ln| a/2+h| is ln((|a||a+2h|)/4)