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

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

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

simplify

3 ln ∣ x + 2 ∣ + 2 ln ∣ x - 2 ∣

ln (∣ x + 2 ∣^{3} (x - 2)^{2})

Solution steps

3 ln ∣ x + 2 ∣ + 2 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}) + 2 ln ∣ x - 2 ∣

Apply log rule:

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

2 ln ∣ x - 2 ∣ = ln (∣ x - 2 ∣^{2})

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

Apply log rule:

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

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

= ln (∣ x + 2 ∣^{3} ∣ x - 2 ∣^{2})

∣ x - 2 ∣^{2} = (x - 2)^{2}

= ln (∣ x + 2 ∣^{3} (x - 2)^{2})

8.314 \cdot 298 \cdot (ln (0.03 3^{5}) - ln (0.74 9^{5}))

ln (\frac{1}{4 x - 10})

ln (\frac{3.64}{23}) + \frac{2 \cdot 2}{23}

(4186) ln (0.77090493) - 8.314 ln (0.1)

ln (y^{x} e^{- y})

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