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One last log law question. little more trickier.

  1. Oct 14, 2009 #1
    1. The problem statement, all variables and given/known data
    [tex]10^{log_{100}4}[/tex] Evaluate.

    I'm on a school computer, i cannot see TEX images. Sorry if their not 100% correct.

    3. The attempt at a solution

    I solved this answer, and got 2. i did this by making the above equation:

    then using a log law to get 4 to the power of 1/2 and solved for 2 using the "double base rule"

    I was told their was a way to do the same thing, but for the exponent and not the base.

    how do you solve: [tex] 10^{log_{10^2}4} [/tex] somehow it still gives a power of 1/2 to the value 4 but i don't understand how to put it there.

    i tried putting it in exponential form:

    [tex] 10^{2x} = 4 [/tex]

    and i guess ed by dividing both exponents by 2 to get:

    [tex] 10^x = 4^{\frac{1}{2}} [/tex]

    but 10 and 4 arent the same base. Is this correct?

  2. jcsd
  3. Oct 14, 2009 #2
    Maybe you can use the identity:

    [tex]\log_{100} x=\frac{\log_{10} x}{\log_{10} 100}[/tex]

  4. Oct 14, 2009 #3


    Staff: Mentor

    And in Donaldos's formula, log10100 = 2.
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