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Solving for a constant in a power

  1. Aug 17, 2008 #1
    1. The problem statement, all variables and given/known data

    Hi all, this isn't exactly a homework question (I'm a law student long out of high school maths!) but has arisen in the context of some of my legal work analysing the difference in height of windspeeds re: wind turbines.

    The "problem" is solve for the constant z0.

    2. Relevant equations

    The main formula is as follows:

    vh = vref . (h/href)^(1/(ln(h/z0)), where vh = velocity at desired height, vref = velocity at measured height, h = desired height, href = measured height, z0 = aerodynamic roughness.

    After inserting a known answer from a previous calculation, the formula reduces to:

    (6.4/4.56) = 13.125^(1/(ln(105/z0))

    3. The attempt at a solution

    As I stated earlier, I'm a couple of years out of high school maths and cannot remember for the life of me how to solve for powers involving logs themselves. I can barely remember the simplest of log rules.

    Any help would be much appreciated.

    Many thanks all,
  2. jcsd
  3. Aug 17, 2008 #2


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    Science Advisor
    Homework Helper

    Welcome to PF!

    Hi Anti-alias ! Welcome to PF! :smile:

    Let's see … 6.4/4.56 = 1.4035.

    So 1.4035 = 13.125(1/(ln(105) - ln(z0)))

    = e(ln(13.125))(1/(ln(105) - ln(z0)))

    so ln(1.4035) = (ln(13.125))/(ln(105) - ln(z0))

    so (ln(105) - ln(z0) = ln(13.125)/ln(1.4035)

    so ln(z0) = ln(105) - ln(13.125)/ln(1.4035)

    so z0 = 105/eln(13.125)/ln(1.4035) :smile:
  4. Aug 17, 2008 #3
    You're a legend tiny tim, huge thanks :approve:
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