What is 1/32 ln(x+2)-1/32 ln(x-2) ?

The solution to 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 :

lo g_{9} ((\frac{8 ^{5}}{11})^{4})

4 lo g_{5} (x) - 6 lo g_{5} (y)

\frac{d}{d x} (cos (2 ln (x))) + \frac{107}{5 ( x )}

lo g_{15} (\frac{17 - 4 x}{2}) + e^{x^{2} - x - 2}

ln (2 e^{3 x})

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