Slide rule(exponential and logarithm)?

Question

1 2 4 8 16 32 64 128 . imagine it is numbers in a rule. the question is estimate the positions of 5,25,10,20,40,50,80 n 3. i think the positions can be find by diving the place.eg. 2,3,4 then 8-4=4 n then divide by 2 u get 6 so you can estimate where is 5,6, or 7. my question is what there is got to do with exponential or logarithm. basically, you can find the number positions by dividing them. if the area is big, you have divide many times n then you can find the position. if anyone understand the link between exponential or logarithm with the position estimation question pls help me

Answer 1

With the powers of 2 evenly spaced on a rule, 1, 2, 4, ... The rule could be used as a simple slide rule. But, as you say, where do you place the numbers in between? The positions on the rule represent powers of two, so the six, for example would be placed at a point which equals the exponent you would have to put on 2 to get 6. That can be found using your calculator and this formula:
logb(x) = logk(x)/logk(b)
You can use either the natural log key, ln, or log base ten, log. But be consistent. Here's what you would do for 6:
log2(6) = ln(6)/ln(2) = 2.585, say 2.59. So the 6 is 59/100'ths of the way from the 4 to the 8. Not half way as you seem to suggest in your description.All the numbers you have listed can be located using the method described above.
To use this as a slide rule, you would need two identically calibrated rules, and you would multiply, for example, by adding segments that represent exponents of 2.

Answer 2

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