What is ln|(x+5)/2+1|-ln|(x+5)/2-1| ?

The solution to ln|(x+5)/2+1|-ln|(x+5)/2-1| is ln((|x+7|)/(|x+3|))

Popular >

simplify ln|(x+5)/2+1|-ln|(x+5)/2-1|

simplify

ln \frac{x + 5}{2} + 1 - ln \frac{x + 5}{2} - 1

ln (\frac{∣ x + 7 ∣}{∣ x + 3 ∣})

Solution steps

ln \frac{x + 5}{2} + 1 - ln \frac{x + 5}{2} - 1

Apply log rule:

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

ln \frac{x + 5}{2} + 1 - ln \frac{x + 5}{2} - 1 = ln (\frac{\frac{x + 5}{2} + 1}{\frac{x + 5}{2} - 1})

= ln (\frac{\frac{x + 5}{2} + 1}{\frac{x + 5}{2} - 1})

Simplify

\frac{\frac{x + 5}{2} + 1}{\frac{x + 5}{2} - 1} : \frac{∣ x + 7 ∣}{∣ x + 3 ∣}

= ln (\frac{∣ x + 7 ∣}{∣ x + 3 ∣})

ln (\frac{8}{6})

ln (\frac{e ^{x^{2} c o s (x)}}{2 x + 4})

ln (x + 7) - 2 ln (x - 3) + ln (7)

ln (5) + 1 + ln (y) - 7 ln (x)

ln (\frac{e ^{8}}{19})

What is ln|(x+5)/2+1|-ln|(x+5)/2-1| ?
The solution to ln|(x+5)/2+1|-ln|(x+5)/2-1| is ln((|x+7|)/(|x+3|))