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Power raised to a logarithm question

  1. Nov 8, 2013 #1
    1. The problem statement, all variables and given/known data
    Solve for x
    7^log(base: 7) 3 = x

    2. Relevant equations



    3. The attempt at a solution
    Ans is 3
    Can someone explain to me how to solve for powers raised to a log like this one?
     
  2. jcsd
  3. Nov 8, 2013 #2

    jedishrfu

    Staff: Mentor

    y = 10 ^ x then log y = x right ?

    looking at log y = x then 10 ^ log y = 10 ^ x

    but 10 ^ x is y so

    10 ^ log y = y

    now since 10 is the base follow the same logic with base 7
     
  4. Nov 8, 2013 #3
    in which grade are you??
     
  5. Nov 8, 2013 #4

    D H

    User Avatar
    Staff Emeritus
    Science Advisor

    7x is a function: for every real number x, 7x has a single, well-defined value. Denote this function as f(x): f(x)=7x. Rhetorical question: What's the inverse of this function? The answer is log base 7. Denote this as f-1(x)=log7x.

    A non-rhetorical question: Given *any* function f(x) and its inverse f-1(x), what is f(f-1(x)) ?
     
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