when writing log b to base a, (log-a(subscript)-b), can a be less than 0?

If you want to restrict the domain to real numbers, negative log bases must be avoided

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In mathematics, the notation log-_ab represents the logarithm of b with base a. The base a must be a positive number and different from 1, which means it must be greater than 0. Consequently, when using this notation, a cannot be less than or equal to 0.

To understand why a cannot be less than 0, let's explore the properties of logarithms. Logarithms are defined for positive numbers, and their bases determine the range of values they can take. Since the logarithm of a positive number is always defined, the base must be a positive number.

When a is negative, the logarithm log_ab would be undefined because there is no real number that can be raised to a negative base to yield a positive result. Therefore, a logarithm with a negative base is not allowed in standard mathematics.

In summary, when writing log_ab, the base a cannot be less than or equal to 0; it must be a positive number.