For which of the following values of b would the logarithm be undefined?

The logarithm function, specifically the common logarithm (base 10) or natural logarithm (base e), is defined only for positive real numbers. Given this, let's examine why b = 1 is not where the logarithm becomes undefined and instead focus on values where it would be.

When considering potential values of b:

• For b = 0, the logarithm is undefined because the logarithm of zero does not exist. You cannot find a number that you can raise to a power to get zero. This is one reason why logarithms are undefined for non-positive numbers.

• For b = 1, the logarithm is defined but is equal to zero, as any logarithm of 1 is 0, regardless of the base. Therefore, this option does not indicate an undefined logarithm.

• For b = -1, the logarithm is also undefined because logarithms cannot take negative numbers as input. There is no exponent that you can raise a positive number to in order to produce a negative result, which makes the logarithm for negative values undefined.

The option indicating that there are no values of b for which the logarithm is undefined would not be accurate because both b = 0 and b = -1 lead