Math 2
posted by Eric on .
Last one I promise. I'm having trouble with these.
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

ln 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