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This log equation

  1. Apr 11, 2009 #1
    1. The problem statement, all variables and given/known data

    2.3(1.2)^5z = 3(4.1)^z solve for z

    2. Relevant equations

    the properties of logarithm

    3. The attempt at a solution
    okay I first divided the 3 with 2.3 and got 1.304 then i brough the 5z and the z down which gives me 5z log(1.2)=1.304 z log(4.1) then i plugged log of 1.2 and 4.1 into the calculator and got .079 and .613 which makes the equation 5z(.079)=1.034z(.613) i then distributed and got .395z=.8z which doesnt give me an answer is the answer no solutions or did i do sumthing wrong?
     
  2. jcsd
  3. Apr 11, 2009 #2
    Hint: log( A B^z ) = log(A) + log(B^z) = log(A) + z log(B)
     
  4. Apr 12, 2009 #3
    Yes, there are no solutions to this equation. Unless you used z because you want complex solutions, in which case the properties of logarithms aren't the same.
     
  5. Apr 13, 2009 #4
    There is most definitely a solution to this equation. Take giant_bog's advice in using that log expansion rule.
     
  6. Apr 13, 2009 #5
    You are correct. My mistake.
     
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