Logarithmic Scale - Estimating Values in A Diagram With Logarithmic Scale

Estimating Values in A Diagram With Logarithmic Scale

One method for accurate determination of values on a logarithmic axis is as follows:

1. Measure the distance from the point on the scale to the closest decade line with lower value with a ruler.
2. Divide this distance by the length of a decade (the length between two decade lines).
3. 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:

1. Measure the distance between consecutive decades with a ruler. You can use any units provided that you are consistent.
2. Take the log (value of interest/nearest lower value decade) multiplied by the number determined in step one.
3. 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).