log10xk

log10xk is not a standard mathematical notation and its meaning is ambiguous without additional context or parentheses. In many contexts it could be interpreted in several ways, such as the base-10 logarithm of the product xk, the base-10 logarithm of the power x^k, or the logarithm of a single variable named xk.

One common reading is log10(xk), where xk denotes the product of two positive quantities x and k. In this interpretation, log10(xk) equals log10(x) + log10(k) whenever x > 0 and k > 0, due to the property log(ab) = log(a) + log(b). For example, log10(2 × 5) = log10(10) = 1.

Another reading is log10(x^k), the logarithm of x raised to the power k. In this case, log10(x^k) = k · log10(x) for x > 0. This form is commonly written as log10(x^k) with explicit parentheses; missing parentheses can lead to confusion with the product interpretation above.

A third possibility is that xk is simply a variable name (for instance, a variable “xk” in a model). Then the expression represents the logarithm of that variable, defined wherever xk > 0.

Practical guidance: to avoid ambiguity, use explicit notation such as log10(xk) for the product, log10(x^k) for the power, or log10(x_k) if xk is an indexed variable. In programming, always include parentheses to clarify the intended operation, e.g., log10(x * k) versus log10(x ** k). Remember that the domain for all forms is typically the positive real numbers where the logarithm is defined.