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

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

Popular >

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

simplify

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Combine same powers :

\frac{( ln ( 96 ) - ln ( 3 ) )}{2}

5 ln (x - 8) - 4 ln (x)

lo g_{10} (\frac{x ^{3} y ^{4}}{z ^{3}})

\frac{1}{3} (ln (x) + ln (x - 6) - ln (x^{3} + 9))

\frac{1}{2} lo g_{10} (x + 3) + \frac{1}{2} lo g_{10} (2 x - 1)

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