What is 1/4 ln(x+2)-1/4 ln(x-2) ?

The solution to 1/4 ln(x+2)-1/4 ln(x-2) is ln(\sqrt[4]{(x+2)/(x-2)})

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simplify 1/4 ln(x+2)-1/4 ln(x-2)

simplify

\frac{1}{4} ln (x + 2) - \frac{1}{4} ln (x - 2)

Solution steps

\frac{1}{4} ln (x + 2) - \frac{1}{4} ln (x - 2)

Apply log rule:

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

\frac{1}{4} ln (x + 2) = ln ((x + 2)^{\frac{1}{4}})

= ln ((x + 2)^{\frac{1}{4}}) - \frac{1}{4} ln (x - 2)

Apply log rule:

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

\frac{1}{4} ln (x - 2) = ln ((x - 2)^{\frac{1}{4}})

= ln ((x + 2)^{\frac{1}{4}}) - ln ((x - 2)^{\frac{1}{4}})

Apply log rule:

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

ln ((x + 2)^{\frac{1}{4}}) - ln ((x - 2)^{\frac{1}{4}}) = ln (\frac{( x + 2 ) ^{\frac{1}{4}}}{( x - 2 ) ^{\frac{1}{4}}})

= ln (\frac{( x + 2 ) ^{\frac{1}{4}}}{( x - 2 ) ^{\frac{1}{4}}})

Combine same powers :

ln (\frac{273.15}{262.05})

ln (2) + 5 ln (x - 1) - 2 ln (x + 3)

2 ln (x - 4) - ln (x + 4) - ln (x^{2} - 16) + ln (4) + ln (x)

ln (x) + ln (y) + \frac{x \frac{d y}{d x} + y}{y}

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

What is 1/4 ln(x+2)-1/4 ln(x-2) ?
The solution to 1/4 ln(x+2)-1/4 ln(x-2) is ln(\sqrt[4]{(x+2)/(x-2)})