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Multiple exponents for logarithms

  1. Feb 22, 2017 #1
    • Member warned that some effort must be shown
    1. The problem statement, all variables and given/known data
    2^(t-1) * 6^(t-2) = 20,000

    2. Relevant equations


    3. The attempt at a solution
    I have no idea how to solve this, although I do understand the basics of logarithms
     
  2. jcsd
  3. Feb 23, 2017 #2

    Mark44

    Staff: Mentor

    One possibility is to take the ##\log_2## of both sides of the equation.
     
  4. Feb 23, 2017 #3

    haruspex

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    Could you find x given axbx=c?
     
  5. Feb 23, 2017 #4
    would it be

    log(a^b^c) = x * x ?
     
  6. Feb 23, 2017 #5

    Mark44

    Staff: Mentor

    This is not even remotely close. You need to review the properties of exponents. A web search on "properties of exponents" or "laws of exponents" should be enlightening.
     
  7. Feb 23, 2017 #6
    One of the properties I found is :

    x^a * x^b = x^(a+b)

    but how would I use that property since I have two different coefficient values?
     
  8. Feb 23, 2017 #7

    haruspex

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    That is not the property you need here.
    Let me ask a different question... how else might you write (xy)a?
     
  9. Feb 23, 2017 #8

    ehild

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    You can write 2t-1=2t * 2-1 and 6t-2=6t * 6-2.
     
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