In applied mathematics, a transcendental equation is an equation over the real (or complex) numbers that is not algebraic, that is, if at least one of its sides describes a transcendental function. Examples include:

A transcendental equation need not be an equation between elementary functions, although most published examples are.

In some cases, a transcendental equation can be solved by transforming it into an equivalent algebraic equation. Some such transformations are sketched below; computer algebra systems may provide more elaborated transformations.

In general, however, only approximate solutions can be found.

Ad hoc methods exist for some classes of transcendental equations in one variable to transform them into algebraic equations which then might be solved.

If the unknown, say x, occurs only in exponents:

If the unknown x occurs only in arguments of a logarithm function:

If the unknown x occurs only as argument of trigonometric functions: