Calculator problem

Discussion in 'Math' started by Mark44, Apr 28, 2008.

  1. Mark44

    Thread Starter Well-Known Member

    Nov 26, 2007
    626
    1
    Someone hands you a scientific calculator with a number (nonzero) showing in its display.

    What keys should you press to cause the calculator to display half the original number?

    To make it just a bit more challenging, you can't use any of the digit keys (0 through 9), nor any of the arithmetic keys (+, -, *, or /).

    Mark
     
  2. mygumballs

    New Member

    Apr 28, 2008
    6
    0
    take that number on the screen and use the e^x function to calculate it's exponential. then take that result and calculate the squareroot of that with the square root button. then take the natural log of that result with the ln button. the result should be the original number divided by two.

    in other words:
    x/2 = ln(sqrt(e^(x)))
     
  3. Caveman

    Active Member

    Apr 15, 2008
    471
    0
    Start with x.
    1. Take the inverse log. => 10^(x)
    2. Take the square root. => SQRT(10^(x)) = (10^x)^(-1/2) = 10^(x/2)
    3. Take the log => x/2
     
  4. Dave

    Retired Moderator

    Nov 17, 2003
    6,960
    144
    That's the way I would answer this. The caveat is that most calculators today expect the function before the number - so, if x is on the screen and you press the inverse log (or any other function) you end up with a Syntax Error!!

    Dave
     
  5. Caveman

    Active Member

    Apr 15, 2008
    471
    0
    Works on the windows calculator.
     
  6. mygumballs

    New Member

    Apr 28, 2008
    6
    0

    that's the case with my current scientific calculator, but i presumed we'd be allowed to use the "ANS" button for this problem. if your calculator has it, that is.
     
  7. Dave

    Retired Moderator

    Nov 17, 2003
    6,960
    144
    Just tried on my Casio FX-83MS and the ANS option doesn't work. If x = 10, then I get an expression "10Ans10" which gives a Syntax Error! There is always M+ (or MR as it is on older calculators), then we can use 10 > M+ > AC > 10^x > RCL > =

    So easy when you know how!

    Dave
     
  8. Dave

    Retired Moderator

    Nov 17, 2003
    6,960
    144
    How do you do the square-root operation on the Windows Calculator without using the numbers 0-9? IIRC there is no sqrt button in scientific mode and the only way to square-root is by raising to the power 0.5. The standard mode doesn't have the log functions.

    Dave
     
  9. flubbo

    Member

    Apr 21, 2008
    25
    0
    The solution is in using logarithms, like both mygumballs and Caveman said.

    Start by taking the anti-logarithm (in any base)

    Then, take the square root

    then, take the logarithm in the same base.

    example:
    Let's say the calculator had 4 in the display

    pressing 10^x yields 10000
    pressing Sqrt(x) yields 100
    pressing Log(x) yields 2 (Q.E.D.)

    Now, let's put 4 back in the display

    pressing e^x yields 54.59815003
    pressing sqrt(x) yields 7.389056099
    pressing ln(x) yields 2 (Q.E.D.)

    @Dave:
    On the Windows Calculator in scientific mode, ticking the "Inv" checkbox (upper left hand corner) allows you to access the inverse functions. (srqt, e^x, etc)

    Let's do it with the Windows Calculator:

    First, select Scientific Mode from the <View> menu.

    then put 4 into the calculator

    Tick the "Inv" checkbox and click Ln
    Tick the "Inv" checkbox and click x^2
    then, just click Ln.

    The display should say 2 (Q.E.D.)

    It's not readily visible, but, the functionality is there. :)

    All The best,
    :Flubbo.
     
  10. Mark44

    Thread Starter Well-Known Member

    Nov 26, 2007
    626
    1
    You guys are pretty quick! I thought it would take you longer than this. The first ones to solve this problem were mygumballs and Caveman, with slightly different but equivalent solutions.

    Mark
     
  11. Dave

    Retired Moderator

    Nov 17, 2003
    6,960
    144
    Well there you go. Shows you how much I use the Windows Calculator!

    Dave
     
  12. K8MHZ

    New Member

    Jun 1, 2008
    6
    0
    I am so lost.....

    My calculator came from the dollar store. FWIW, the first calculator I ever saw that could do what my dollar store calculator can do was in 1974. It cost over 300 dollars in 1974 dollars, well over a grand in today's peso based dollars.

    My phone has one too, but when I tried to solve the problem I got connected to a Microsoft Tech Support operator in India who said his name was Ken asking me what operating system I had.
     
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