Log10nlog102

Log10nlog102 is not a standard mathematical term or constant. It appears to combine the base-10 logarithm operator log10, the variable n, and the base-10 logarithm of 2. The most straightforward interpretation in many contexts is the product log10(n) · log10(2).

Under this interpretation, the expression is defined for n > 0 since log10(n) requires a positive argument. The constant log10(2) ≈ 0.30102999566 is positive, so the product shares the sign of log10(n). Therefore the value is negative when 0 < n < 1, zero at n = 1, and positive for n > 1. Because log10(n) is increasing for n > 0 and log10(2) is a positive constant, the product log10(n) · log10(2) is an increasing function on (0, ∞).

If the intended meaning were log10(n log10(2)) or log10(n log10 2) without parentheses, standard logarithm rules would apply differently: log10(n log10(2)) = log10(n) + log10(log10(2)). Since log10(2) is about 0.30103, log10(log10(2)) ≈ log10(0.30103) ≈ −0.52144. In that interpretation, the expression equals log10(n) − 0.52144… and would be defined for n > 0 as well.

There is no widely used constant or notation that exactly matches "log10nlog102," so precise notation is important. In practice, authors would write log10(n) · log10(2) to indicate multiplication, or log10(n log10(2)) to denote a single logarithm of a product.