In the logarithm notation log_b(a), what does the symbol b represent?

In the logarithm notation log_b(a), what does the symbol b represent?

• A. The exponent
• B. The base of the logarithm
• C. The argument
• D. The result

Answer: (B)

The symbol b is the base of the logarithm—the number you raise to a power. In log_b(a), you’re asking: what exponent must you apply to b to obtain a? So b serves as the base, not the exponent, the argument, or the result. For example, log_3(81) = 4 because 3^4 = 81. Here, a is the argument, and the result (the value of the logarithm) is the exponent that makes the equation true. The base must be positive and not equal to 1 for the logarithm to be well-defined.

The symbol b is the base of the logarithm—the number you raise to a power. In log_b(a), you’re asking: what exponent must you apply to b to obtain a? So b serves as the base, not the exponent, the argument, or the result. For example, log_3(81) = 4 because 3^4 = 81. Here, a is the argument, and the result (the value of the logarithm) is the exponent that makes the equation true. The base must be positive and not equal to 1 for the logarithm to be well-defined.