log20log3

Log20log3 is not a standard mathematical symbol, and its meaning is ambiguous without additional context. In many informal writings it is read as the product of two logarithms: log(20) times log(3), where the base is implied by convention.

If the base is 10 (common logarithms), log10(20) ≈ 1.30103 and log10(3) ≈ 0.477121. Their product is approximately 0.6207487. If the base is e (natural logarithms), ln(20) ≈ 2.99573 and ln(3) ≈ 1.09861, giving a product of about 3.289. More generally, for any base b, log_b(20) · log_b(3) = (ln 20 · ln 3) / (ln b)^2.

A different interpretation arises if the expression is intended as a nested logarithm, such as log_20(log_3(x)). In that form, an inner argument x is required; without it the expression is incomplete. For example, with x = 10, log_3(10) is a finite number, and then one can take log_20 of that result. Without a specified argument, however, the value cannot be determined.

Because of these ambiguities, precise notation is important. To avoid confusion, one should specify the base of the logarithms and whether the expression represents a product or a composition, for example log_10(20) · log_10(3) or log_20(log_3(x)). See also fundamental logarithm properties and base change.