log

Use the log function in APL to compute the natural logarithm (base-e) of a positive numeric value. The function is the inverse of exp.

log is one of the most commonly used mathematical functions in observability. Log-transforming latency, error counts, or request rates compresses wide value ranges into a more manageable scale, reduces the influence of extreme outliers, and can reveal patterns that are linear on a log scale. It's also the basis for computing geometric means with exp(avg(log(x))).

Usage

Syntax

log(x)

Parameters

Returns

• The natural logarithm of x.
• null if x is negative, zero, or can't be converted to a real value.

Example

Use log to compress request durations onto a natural log scale.

Query

['sample-http-logs']
| where req_duration_ms > 0
| extend log_duration = log(req_duration_ms)
| project _time, id, req_duration_ms, log_duration

Output

List of related functions

• exp: Returns e^x. Use it as the inverse of log to return to the original scale.
• log2: Returns the base-2 logarithm. Use it for binary-scale analysis such as bit depth or memory sizing.
• log10: Returns the base-10 logarithm. Use it for order-of-magnitude analysis or decibel calculations.
• loggamma: Returns the log of the absolute value of the gamma function. Use it to avoid overflow when computing gamma on large inputs.
• sqrt: Returns the square root. Use it as a lighter alternative to log for compressing small value ranges.

Other query languages