📊 Logarithm & Antilogarithm Tables

Complete reference tables (Base 10) for mathematical calculations

90

Log Rows (10-99)

100

Antilog Rows (.00-.99)

4-Digit

Precision

📌 Logarithm Table (Base 10): Find the mantissa of log₁₀(x). Row = first two digits, Column 0-9 = third digit, Mean differences = fourth digit interpolation.

N	0	1	2	3	4	5	6	7	8	9	Mean Differences
											1	2	3	4	5	6	7	8	9

📌 Antilogarithm Table (Base 10): Find the number from a given mantissa. Row = first two decimal digits, Column 0-9 = third digit, Mean differences = fourth digit.

.x	0	1	2	3	4	5	6	7	8	9	Mean Differences
											1	2	3	4	5	6	7	8	9

How to Use These Tables

1️⃣ Finding a Logarithm (Log Table)

Example: Find log₁₀(12.34)

1. Find row 12 (first two significant digits)
2. Look at column 3 (third digit) → Value: 0899
3. Add mean difference for 4 (fourth digit) → 14
4. Result: 0899 + 14 = 0913, so log(12.34) = 1.0913

2️⃣ Finding an Antilogarithm (Antilog Table)

Example: Find antilog(0.0913)

1. Take mantissa: .0913 → Look at row .09
2. Find column 1 (third digit) → Value: 1023
3. Add mean difference for 3 → 1
4. Result: 1023 + 1 = 1024, which means 1.024 (with proper decimal placement)

📊 Common Applications

• Multiplication: log(A × B) = log(A) + log(B)
• Division: log(A ÷ B) = log(A) - log(B)
• Powers: log(Aⁿ) = n × log(A)
• Roots: log(∜A) = (1/4) × log(A)

💡 Tips

• Mean differences help with interpolation for the 4th significant digit
• The characteristic (integer part) comes before the decimal
• All table values are mantissas (fractional part only)
• Use smooth interpolation between table values for higher precision