Question

Explain why log₄ (log 0.3) is undefined.

A. Logarithms of negative numbers are undefined.
B. Logarithms of zero are undefined.
C. Logarithms of non-integer values are undefined.
D. Logarithms of fractions are undefined.

Answer 1

The logarithm of zero is undefined.

Step-by-step explanation:

The expression log₄(log 0.3) is undefined, and the explanation lies in the properties of logarithms. In the given expression, the outer logarithm is base 4 (log₄), and the inner logarithm is base 10 (log). Logarithms are undefined for non-positive arguments. The logarithm of zero is undefined, and in this case, log 0.3 is a positive value, but it is less than 1. Therefore, the correct explanation is: B. Logarithms of zero are undefined. The expression log₄(log 0.3) is undefined because the inner logarithm log 0.3 is less than 1, and the logarithm of a value less than 1 is undefined in the real number system.