Math 2

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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

  • Math 2 -

    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

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