What is ln| r/2+1|-ln| r/2-1| ?

The solution to ln| r/2+1|-ln| r/2-1| is ln((|r+2|)/(|r-2|))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

simplify

ln \frac{r}{2} + 1 - ln \frac{r}{2} - 1

ln (\frac{∣ r + 2 ∣}{∣ r - 2 ∣})

Solution steps

ln \frac{r}{2} + 1 - ln \frac{r}{2} - 1

Apply log rule:

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

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

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

Simplify

\frac{\frac{r}{2} + 1}{\frac{r}{2} - 1} : \frac{∣ r + 2 ∣}{∣ r - 2 ∣}

= ln (\frac{∣ r + 2 ∣}{∣ r - 2 ∣})

ln 3 - 2 - ln - 3 - 2

\frac{7 ln ( 2 ) - ln ( 12.8 )}{ln ( 36.1 ) - ln ( 22 )}

ln (9 e^{2}) + ln (3 e^{- 2})

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

What is ln| r/2+1|-ln| r/2-1| ?
The solution to ln| r/2+1|-ln| r/2-1| is ln((|r+2|)/(|r-2|))