Dimensional Analysis
In dimensional analysis, transcendental functions are notable because they make sense only when their argument is dimensionless (possibly after algebraic reduction). Because of this, transcendental functions can be an easy-to-spot source of dimensional errors. For example, log(10 m) is a nonsensical expression, unlike log(5 meters / 3 meters) or log(3) meters. One could attempt to apply a logarithmic identity to get log(10) + log(m), which highlights the problem: applying a non-algebraic operation to a dimension creates meaningless results.
Read more about this topic: Transcendental Function
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