What is simplify-3ln|x+2|+x-ln|x-2| ?

The solution to simplify-3ln|x+2|+x-ln|x-2| is -ln(|x+2|^3|x-2|)+x

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simplify-3ln|x+2|+x-ln|x-2|

simplify

- 3 ln ∣ x + 2 ∣ + x - ln ∣ x - 2 ∣

- ln (∣ x + 2 ∣^{3} ∣ x - 2 ∣) + x

Solution steps

- 3 ln ∣ x + 2 ∣ + x - ln ∣ x - 2 ∣

Apply log rule:

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

3 ln ∣ x + 2 ∣ = ln (∣ x + 2 ∣^{3})

= - ln (∣ x + 2 ∣^{3}) + x - ln ∣ x - 2 ∣

Rewrite

- ln (∣ x + 2 ∣^{3}) - ln ∣ x - 2 ∣

- (ln (∣ x + 2 ∣^{3}) + ln ∣ x - 2 ∣)

= - (ln (∣ x + 2 ∣^{3}) + ln ∣ x - 2 ∣) + x

Apply log rule:

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

ln (∣ x + 2 ∣^{3}) + ln ∣ x - 2 ∣ = ln (∣ x + 2 ∣^{3} ∣ x - 2 ∣)

= - ln (∣ x + 2 ∣^{3} ∣ x - 2 ∣) + x

ln (\frac{e ^{x}}{sin ( x ) ( x - 2 ) ^{2}})

ln (\frac{e ^{X^{2}} cos ( X )}{2 X})

\frac{1}{2} (ln (6) + ln (2))

lo g_{e} (\frac{( 4300 )}{3})

ln (\frac{190 ( 200 - 190 )}{3600})

What is simplify-3ln|x+2|+x-ln|x-2| ?
The solution to simplify-3ln|x+2|+x-ln|x-2| is -ln(|x+2|^3|x-2|)+x