Question

Select the correct answer. What is the solution set to this equation? \( \log_4(3) \log_1x = 1 \)?

a. \( x = -3 \) and \( x = 0 \)
b. \( x = 1 \)
c. \( x = 1 \) and \( x = -4 \)
d. \( 2 = 0 \)

Answer 1

The equation \( \log_4(3) \log_1x = 1 \) contains a logarithm base 1, which is undefined. Hence, this equation does not have a valid solution set.

Step-by-step explanation:

The equation presented is \( \log_4(3) \log_1x = 1 \). First, we should remind ourselves that the logarithm base 1 is undefined as it represents an infinitive situation since any number to the power of 0 equals 1. Therefore, the equation \( \log_4(3) \log_1x = 1 \) is not valid because \( \log_1x \) does not have a value.

The correct approach to solve a logarithmic equation is to isolate the variable and then exponentiate both sides using the base of the logarithm, if necessary. However, in this case, the equation cannot be solved because of the invalid logarithm base 1.