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September 22, 2014

September 22, 2014

Posted by **Eric** on Wednesday, April 24, 2013 at 4:15pm.

Express in terms of logarithms of x, y, z, or w.

ln 4th root (x^6/(y^2 z))

Write the expression as one logarithm.

ln y^4 + (1/3) ln(x^9 y^9) − 7 ln y

- Math 2 -
**Reiny**, Wednesday, April 24, 2013 at 6:21pmln 4th root (x^6/(y^2 z))

I read that as

ln (x^6/(y^2z)^(1/4)

= (1/4) ( ln x^6 - ln y^2 - ln z)

= (1/4)( 6lny - 2lny - lnz)

= (3/2)lny - (1/2)lny - (1/4) lnz

ln y^4 + (1/3) ln(x^9 y^9) − 7 ln y

= ln y^4 + ln(x^9 y^9)^3 - ln y^7

= ln [y^4(x^3 y^3)/y^7]

= ln (x^3) or 3lnx

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