Estimating Values in A Diagram With Logarithmic Scale
One method for accurate determination of values on a logarithmic axis is as follows:
- Measure the distance from the point on the scale to the closest decade line with lower value with a ruler.
- Divide this distance by the length of a decade (the length between two decade lines).
- The value of your chosen point is now the value of the nearest decade line with lower value times 10a where a is the value found in step 2.
Example: What is the value that lies halfway between the 10 and 100 decades on a logarithmic axis? Since it is the halfway point that is of interest, the quotient of steps 1 and 2 is 0.5. The nearest decade line with lower value is 10, so the halfway point's value is (100.5) × 10 = 101.5 ≈ 31.62.
To estimate where a value lies within a decade on a logarithmic axis, use the following method:
- Measure the distance between consecutive decades with a ruler. You can use any units provided that you are consistent.
- Take the log (value of interest/nearest lower value decade) multiplied by the number determined in step one.
- Using the same units as in step 1, count as many units as resulted from step 2, starting at the lower decade.
Example: To determine where 17 is located on a logarithmic axis, first use a ruler to measure the distance between 10 and 100. If the measurement is 30mm on a ruler (it can vary — ensure that the same scale is used throughout the rest of the process).
- × 30 = 6.9
x = 17 is then 6.9mm after x = 10 (along the x-axis).
Read more about this topic: Logarithmic Scale
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