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

The solution to 1/2 ln(y)-1/2 ln(y+2) is ln(sqrt(y/(y+2)))

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

simplify

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

ln (\frac{y}{y + 2})

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Combine same powers :

= ln (\frac{y}{y + 2})

4 ln (\frac{1}{4})

lo g_{6} (\frac{36 y}{x ^{7} z ^{3}})

ln (\frac{5}{x ^{2} + 9})

ln (\frac{575}{500})

lo g_{1.5} (\frac{700}{200}) - 2

What is 1/2 ln(y)-1/2 ln(y+2) ?
The solution to 1/2 ln(y)-1/2 ln(y+2) is ln(sqrt(y/(y+2)))