What is simplify-1/5 ln(y+3)+1/5 ln(y-2) ?

The solution to simplify-1/5 ln(y+3)+1/5 ln(y-2) is ln(\sqrt[5]{(y-2)/(y+3)})

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simplify-1/5 ln(y+3)+1/5 ln(y-2)

simplify

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

\frac{1}{5} ln (y - 2) = ln ((y - 2)^{\frac{1}{5}})

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

Apply log rule:

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

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

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

Combine same powers :

\frac{1}{2} ln (\frac{y}{z})

ln (e^{y} (y - 1))

lo g_{10} (\frac{z}{x ^{5}})

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

ln (\frac{0.892}{0.955})

What is simplify-1/5 ln(y+3)+1/5 ln(y-2) ?
The solution to simplify-1/5 ln(y+3)+1/5 ln(y-2) is ln(\sqrt[5]{(y-2)/(y+3)})