In terms of common logarithms, how is log(x) expressed?

In mathematics, common logarithms refer specifically to logarithms that have a base of 10. This is an important distinction because logarithms can have various bases, such as base e (natural logarithm) or other numbers. The notation log(x) typically implies the common logarithm unless a different base is specified. Thus, when one sees log(x), it is understood to mean log base 10 of x, which can be expressed explicitly as log10(x).

Therefore, expressing log(x) as log10(x) correctly indicates that the logarithm is in base 10, which is the standard interpretation for the common logarithm in scientific and engineering contexts. This understanding is essential for correctly applying logarithmic functions in various mathematical scenarios, particularly in solving equations involving exponential growth or decay, where common logarithms are frequently used.

Other expressions presented do not accurately reflect the definition of the common logarithm. For instance, dividing the logarithm by 10, multiplying it by 10, or expressing it as a logarithm of a function to a power do not maintain the definition of the common logarithm and therefore do not fit its standard representation.