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Multiply Logarithmic Values - Calculator

Multiply logarithms: calculate times with values on a logarithmic scale. Here, the value to be multiplied is provided as a logarithmic value, while the multiplier is a standard linear value. The result is output as a logarithmic value with the same base. To perform the calculation, the logarithmic value is first converted into a linear value. This is then multiplied by the multiplier and subsequently converted back into logarithmic form.
Please specify the base, the logarithmic value, and the linear multiplier. The logarithmic result based on the same base will be output.

Base :
Value:
Multiplier:
Result:

Round to   0 1 2 3 4 5 6 7 8 9 10 11 12 13 14   decimal places.

Example: The Richter scale for earthquakes uses a base of 10. An earthquake of magnitude 5 has a linear value of 10⁵ = 100,000. An earthquake twice as strong has a linear value of 200,000. The common logarithm (base 10 logarithm) of this value is approximately 5.301. Thus, on the logarithmic scale, an earthquake twice as strong does not have double the magnitude, but rather a magnitude of approximately 5.3. 10^5.301 ≈ 200,000.

How the logarithmic value changes through multiplication depends on the multiplier and the base used. With a base of 10, a tenfold increase in the linear value corresponds to an increase of 1 in the logarithmic value. A doubling corresponds to an increase of approximately 0.301. Consequently, changes in linear values ​​appear smaller on a logarithmic scale. This should be kept in mind when dealing with logarithmic values and interpreting them.

The basic formula for multiplying a logarithmic value x by a linear multiplier m is:
log_b(b^x * m) = x + log_b(m)
Here, b is the base of the logarithm, x is the logarithmic value, and m is the multiplier. The result is again a logarithmic value with base b.

Last updated on 10/06/2026. Author: Jürgen Kummer

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