Log10y

Log10y denotes the common logarithm of y, the exponent to which 10 must be raised to obtain y. It is usually written as log10(y) or log10 y. The function is defined for y > 0 and yields a real number.

Equivalently, log10 y = ln y / ln 10, where ln is the natural logarithm. This highlights that log10 y is a monotonic increasing function on (0, ∞). The domain is (0, ∞) and the range is (−∞, ∞).

Some basic identities: log10(1) = 0; log10(10) = 1; log10(ab) = log10 a + log10 b; log10(a^b) = b log10 a. The inverse function of log10 is the exponential base-10 function, 10^x, and log10(10^x) = x, 10^{log10 y} = y.

Change of base and calculation: log10 y can be computed from any logarithm as log_b(y) / log_b(10).

Applications and examples: The common logarithm is used in scientific notation, statistics, and various engineering fields; pH is defined as -log10[H+]. Example: log10(1000) = 3 and log10(0.01) = -2.