slide rule logarithmic scale

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A slide rule is a mechanical analog computer that uses logarithmic scales to perform mathematical calculations like multiplication, division, roots, and logarithms. 

How the Logarithmic Scale Works

On a standard ruler, the marks are evenly spaced (linear scale), so adding lengths means adding numbers. A slide rule uses a logarithmic scale, where the physical distance of a number from the start of the scale is proportional to its logarithm, not its arithmetic value. 

• Logarithmic Spacing: The distance between
  
  and
  
  is the same as the distance between
  
  and
  
  , and between
  
  and
  
  . This is because the distance is based on
  
  
  
  
  :
  • 
    
    
    
    
  • 
    
    
    
    
  • 
    
    
    
    
     
• Multiplying & Dividing: Because
  
  
  
  
  
  
  
  
  
  
  
  
  
  , sliding the rule to add distances together mechanically multiplies the actual numbers. Subtraction works in reverse for division. 

Common Slide Rule Scales

While slide rules can have dozens of specialized scales, you will generally see the following logarithmic scales on most models:

• C and D Scales: The fundamental scales used for multiplication, division, and basic proportions. They usually run from
  
  to
  
  .
• A and B Scales: Used for squaring and square roots. The scale is compressed to show two full logarithmic cycles.
• K Scale: Used for cubes and cube roots, compressing the range into three logarithmic cycles.
• L Scale: A special, purely linear scale that represents the actual logarithm (the mantissa) of a number. By aligning numbers on the D scale with the L scale, you can quickly read the base-10 logarithm. 

For a visual breakdown and practical demonstration of how to read and use the logarithmic (L) scale on your slide rule, check out this quick tutorial:

2m

Slide Rule - Logs

7.6K views · Dec 6, 2019

YouTube · Logan West

• Why L? -- the log scale explained

  Jun 22, 2016 — and um what they're useful for and why there is a logarithm base 10 scale on your slide rule which you think you never really are ...

  

  11m

  

  

  YouTube·Professor Herning
• Slide Rule - Logs

  Dec 6, 2019 — look quickly at some logs. so if you look at the Dcale. here you can put the cursor on a number and read off the value on the L sc...

  

  2m

  

  

  YouTube·Logan West
• How do slide rules use logarithms to perform calculations?

  Jan 15, 2014 — Take the logarithms of the two numbers to be multiplied together (log(a), log(b)) Add the logarithms together (log(a) + log(b), wh...

  

  

  Reddit·r/askscience

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