What is simplify-1/32 ln|x+2|+1/32 ln|x-2| ?

The solution to simplify-1/32 ln|x+2|+1/32 ln|x-2| is ln(\sqrt[32]{(|x-2|)/(|x+2|)})

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simplify-1/32 ln|x+2|+1/32 ln|x-2|

simplify

- \frac{1}{32} ln ∣ x + 2 ∣ + \frac{1}{32} ln ∣ x - 2 ∣

Solution steps

- \frac{1}{32} ln ∣ x + 2 ∣ + \frac{1}{32} ln ∣ x - 2 ∣

Apply log rule:

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

\frac{1}{32} ln ∣ x + 2 ∣ = ln (∣ x + 2 ∣^{\frac{1}{32}})

= - ln (∣ x + 2 ∣^{\frac{1}{32}}) + \frac{1}{32} ln ∣ x - 2 ∣

Apply log rule:

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

\frac{1}{32} ln ∣ x - 2 ∣ = ln (∣ x - 2 ∣^{\frac{1}{32}})

= - ln (∣ x + 2 ∣^{\frac{1}{32}}) + ln (∣ x - 2 ∣^{\frac{1}{32}})

Apply log rule:

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

ln (∣ x - 2 ∣^{\frac{1}{32}}) - ln (∣ x + 2 ∣^{\frac{1}{32}}) = ln (\frac{∣ x - 2 ∣ ^{\frac{1}{32}}}{∣ x + 2 ∣ ^{\frac{1}{32}}})

= ln (\frac{∣ x - 2 ∣ ^{\frac{1}{32}}}{∣ x + 2 ∣ ^{\frac{1}{32}}})

Combine same powers :

ln (\frac{( 3 y + 1 ) ^{5}}{y ^{2} + 1})

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

2000 ln (\frac{5}{4})

What is simplify-1/32 ln|x+2|+1/32 ln|x-2| ?
The solution to simplify-1/32 ln|x+2|+1/32 ln|x-2| is ln(\sqrt[32]{(|x-2|)/(|x+2|)})