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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Combine same powers :

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

lo g_{7} (7 m n^{4})

lo g_{10} (\frac{a b ^{7}}{c ^{8}})

lo g_{2} (A B^{2})

ln (\frac{( 3 ^{x} 6 ^{2 x} )}{2 ^{2 x}})

lo g_{6} (\frac{1}{z ^{3}})

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