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Homework Help: Logs and Exponential

  1. Jul 30, 2010 #1
    1. The problem statement, all variables and given/known data

    Greetings - can someone please check my work, many thanks


    2. Relevant equations

    If x = 12.4 Find the value of ... correct to two sig fgures

    8^(4x/3) / log(base 10) (5x-3/x^0)

    3. The attempt at a solution

    = 8^(16 8/15) / log(base 10) (5(12.4)-3 / 1)
    = 4.8 x 10^14 (via calc 4.818429574)

    Many thanks
     
  2. jcsd
  3. Jul 31, 2010 #2

    Mark44

    Staff: Mentor

    This expression, (5x-3/x^0), is ambiguous. Is it (5x - 3)/1 or 5x - (3/1)? If it's the former, you're missing some needed parentheses.
    Neither of these expressions is right. Starting with 8^(4x/3), how did you get 8^(16 8/15)? I'm assuming the part in parentheses is 16 + 8/15. If you substitute 12.4 for x, and multiply by 4/3, what do you get?

    How did you get 4.8 x 10^14? That would be 480,000,000,000,000, nowhere close to 4.818...
     
  4. Jul 31, 2010 #3
    Hi Mark

    For this question - I need to substitute 12.4 into all x values.

    (5x-3/x to the power 0) so if you substitute 12.4 into the x in this part of the equation (12.4^0), yes, you will get (5(12.4)/1).

    Is a substitution question.

    I dont yet understand how to add the Maths chararcters in the Forum.

    Cheers
     
  5. Jul 31, 2010 #4

    Mark44

    Staff: Mentor

    That much is obvious.
    No you don't. Where did the 3 go?

    I still don't know what you mean when you wrote (5x-3/x^0), so please read what I wrote in my previous post more carefully and answer the questions that I asked.
     
  6. Jul 31, 2010 #5
    Really sorry,

    If x = 12.4 Find the value of ... correct to two sig fgures

    8^(4x/3) (divided by sign) log(base 10 subscript) (5x-3/x^0) - this is exactly how the question is written.

    x to the 0 power is 1 so log(base10)(5x-3/1) = log 59

    8 to the power of 4x/3 if you substitute 12.4 into x you get 8 to the power of 16 8/15

    So. 8 to the power of 16 8/15 or (16.533333.) (divided by ) log(base10)(5x-3/1) = log 59.

    Hope that helps - otherwise not sure how I can explain this further.

    If I do this again I get 1.6 x 10^14



    Cheers
     
  7. Aug 1, 2010 #6

    HallsofIvy

    User Avatar
    Science Advisor

    Yes, it reduces to
    [tex]\frac{8^{16.53333..}}{59}[/tex]

    but I do NOT get "1.6 x 10^14" for that.
     
  8. Aug 1, 2010 #7
    Thanks HOI, Im getting two different answers and getting confused.

    Ill have another look at this. Cheers
     
  9. Aug 2, 2010 #8

    Mark44

    Staff: Mentor

    This is a relatively straightforward problem in using a calculator. You shouldn't be getting two answers.
     
  10. Aug 3, 2010 #9
    Thanks Mark, for all your help.

    Cheers
     
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