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Homework Help: Log and Ln Problem - Matching Equations

  1. Jan 5, 2012 #1
    1. The problem statement, all variables and given/known data

    I am trying to prove that the following equations are the same for a client, but keep getting different answers using a calculator.

    2. Relevant equations

    1- Cadmium concentration = e^0.86[In(hardness)]-3.2 μg/L

    2 - Cadmium concentration = 10^0.86[log10(hardness)]-3.2 μg/L

    3. The attempt at a solution

    These are the answers I keep getting:

    Cadmium concentration = e^0.86[In(hardness)]-3.2 μg/L = 0.649361 ug/L

    Cadmium concentration = 10^0.86[log10(hardness)]-3.2 μg/L = 0.010051 ug/L
  2. jcsd
  3. Jan 5, 2012 #2


    Staff: Mentor

    why would you think they are the same if you rewrite a little you'll see why:

    cc = hardness * e^0.86 - 3.2


    cc = hardness * 10^0.86 - 3.2

    to make them the same you need to fix the 0.86 power ie 10^y=e^0.86
  4. Jan 5, 2012 #3


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    e ≈ 2.718281828459...

    So, e ≠ 10 → e^0.86 ≠ 10^0.86, etc.

    However, the display on many calculators does show E rather than 10 when displaying powers of ten, as in the following:

    2.998✕108 will be shown as 2.998E8 .

    Perhaps that's what you are thinking of.
  5. Jan 5, 2012 #4


    Staff: Mentor

    There is no In function - it's ln (LN), short for logarithmus naturalis.
  6. Jan 5, 2012 #5
    What is your hardness value?
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