The expression \log_a(x) represents the logarithm of x with base a. It answers the question: "To what power must a be raised to obtain x?" For example, if a = 10 and x = 100, then \log_10(100) = 2 because 10^2 = 100. Logarithms are useful in various fields, including mathematics, science, and engineering, as they help simplify complex calculations, especially when dealing with exponential growth or decay. The base a must be a positive number not equal to 1, and x must be a positive number for the logarithm to be defined.