By Alexander Rudinski
Updated Aug 30, 2022

The logarithmic mean is a specialized average that is especially useful in fields such as heat transfer and thermodynamics, where it accurately represents temperature differences between two states. While it shares the basic concept of an average—summing values and dividing by a count—it incorporates natural logarithms to capture the geometric nature of the data.

Step 1 – Arrange the Numbers

Write the two numbers you want to average in the order they appear. For example, use 190 followed by 280.

Step 2 – Compute Natural Logarithms

Using a scientific calculator, find the natural logarithms (ln) of each value:

• ln(190) ≈ 5.25
• ln(280) ≈ 5.63

Step 3 – Determine the Numerical Difference

Subtract the smaller number from the larger one:

• 280 – 190 = 90

Step 4 – Find the Logarithmic Difference

Subtract the smaller logarithm from the larger:

• 5.63 – 5.25 = 0.38

Step 5 – Calculate the Logarithmic Mean

Divide the numerical difference by the logarithmic difference, keeping the same order for both terms:

• 90 ÷ 0.38 ≈ 236.84

Thus, the logarithmic mean of 190 and 280 is approximately 236.84.

Tools You’ll Need

• Scientific calculator (or a reliable online calculator)
• Paper and pencil for intermediate steps

Important Note

The logarithmic mean is defined only for two non‑negative, real numbers. For more than two values, a different formula and more advanced mathematics are required.