Calculator problem

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

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)))

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

Caveman said:

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

Click to expand...

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

Works on the windows calculator.

Dave said:

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

Click to expand...

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.

mygumballs said:

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.

Click to expand...

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

Caveman said:

Works on the windows calculator.

Click to expand...

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

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.

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

flubbo said:

@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)

Click to expand...

Well there you go. Shows you how much I use the Windows Calculator!

Dave

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.