Understanding Log-Log Scales
The Post Versalog 1460 includes Log-Log (LL) scales for calculations involving exponential relationships. These scales allow users to calculate powers and roots where the exponent is not limited to whole numbers.
Log-Log scales extend the capability of the slide rule beyond ordinary multiplication, division, squares and cubes.
The Purpose of LL Scales
Normal logarithmic scales are based on the relationship between multiplication and addition of logarithms. Log-Log scales apply another logarithmic relationship to allow calculations involving exponential functions.
- Fractional powers.
- Non-integer roots.
- Exponential growth calculations.
- Scientific and engineering formulas.
Types of LL Scales
The Versalog 1460 contains multiple LL scales because exponential relationships cover a wide numerical range.
The different LL scales allow the user to select the range that provides the best accuracy for the calculation.
Calculating Exponential Values
Log-Log scales are used when a number is raised to a power that is not easily calculated using ordinary scales.
Examples include:
- x²·⁵
- x¹ᐟ³
- exponential growth calculations.
The user selects the appropriate LL scale, aligns the required value and reads the corresponding exponential result.
Using LL Scales
The general procedure is:
- Identify the base number and exponent.
- Select the appropriate LL scale range.
- Locate the base value.
- Apply the exponent relationship.
- Read the result using the cursor.
- Verify the magnitude by estimation.
Decimal Placement
As with all slide rule calculations, the LL scales provide the numerical relationship but do not display decimal points automatically.
The operator must estimate whether the result should be greater than or less than the starting value.
- A power greater than 1 increases the value.
- A fractional power may reduce the value.
- A negative exponent produces a reciprocal result.
Engineering Applications
Log-Log scales are particularly useful in scientific and engineering fields where exponential relationships occur frequently.
- Physical formulas.
- Scientific constants.
- Scaling relationships.
- Growth and decay calculations.
Common Mistakes
- Selecting the wrong LL scale range.
- Confusing LL scales with the L scale.
- Ignoring the exponent relationship.
- Failing to estimate the expected answer.
Recommended Diagrams
- Location of LL scales on the Post Versalog 1460.
- Comparison of L and LL scales.
- Fractional power example.
- Exponential calculation workflow.
Continue Learning
Continue to Versalog 1460 Engineering Calculations.