Find the Domain log base x of -4

Problem

(log_x)(−4)

Solution

1. Identify the components of the logarithmic expression (log_b)(a) where b is the base and a is the argument.

2. Apply the rule for the argument of a logarithm, which states that the argument must be strictly greater than zero (a>0.

3. Evaluate the argument in this specific expression, which is −4

4. Determine if the condition −4>0 can be satisfied. Since −4 is a constant less than zero, the expression is undefined for all real numbers regardless of the value of x

5. Conclude that because the argument requirement is violated, there are no values of x that make the expression valid.

Final Answer

Domain of *(log_x)(−4)=∅

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