The expression "log_b(x)" represents the logarithm of a number x to the base b. It answers the question: "To what power must b be raised to obtain x?" For example, if b is 2 and x is 8, then log_2(8) equals 3, because 2 raised to the power of 3 equals 8. Logarithms are useful in various fields, including mathematics, science, and engineering. They help simplify complex calculations, especially when dealing with exponential growth or decay. Understanding logarithms is essential for solving equations involving exponential functions and for analyzing data that spans several orders of magnitude.