Finding unknown indices

  1. I would be grateful if someone could tell me how to find unknown indices.

    e.g 3^x=9

    (i know it is 2 but i would like to know the process for use with larger numbers).

    Thankyou in advance
  2. jcsd
  3. 3^x=9
    get the log base 3 of both sides
  4. No, you used the fact x=2.

    9 = 3^x

    log 9 = log (3^x)

    log 9 = x log 3

    x = log9/log3 = 2

    log can be to any base as long as they are the same. you will usually find base 10, or base e on your calculator. log base e is usually ln.
  5. 1) 3x=9
    As long as we can think of the relationship between 3 and 9, we can solve this problem without using logarithm, like the one suggested by enslam.

    here are more examples (solve for x)
    2) 5x = 625
    3) 4*5x = 100
    4) 2x = 8

    If you use Logarithm, in the step log9/log3, you need to know the fact that 9 = 3^2 too, unless you use a caculator.
  6. HallsofIvy

    HallsofIvy 40,297
    Staff Emeritus
    Science Advisor

    That's true as long as the "opposite" problem, finding the power, can be done easily- as long as the answer is an integer as in all of your examples.

    To solve, for example 3x= 7, you will need to use logarithms.
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