Evaluate log base 6 of -36

Problem

(log_6)(−36)

Solution

1. Identify the definition of a logarithm. The expression (log_b)(x)=y is equivalent to the exponential form b^y=x

2. Set up the equation for the given problem. We are looking for a value y such that 6^y=−36

3. Analyze the domain of the logarithm function. The argument of a logarithm, x must be a positive real number (x>0 because a positive base raised to any real power always results in a positive value.

4. Determine the existence of a real solution. Since 6^y is always greater than 0 for all real values of y it can never equal −36

5. Conclude that the expression is undefined in the set of real numbers.

Final Answer

(log_6)(−36)=undefined

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