Answer:
no solutions
Step-by-step explanation:
Since the two terms have the same base, we are able to use the rule for subtracting logarithms:
[tex]log_{b}(x) - log_{b}(y) = log_{b}(\frac{x}{y} )[/tex]
Therefore, the equation can be written as:
[tex]log_{6}(\frac{x-6}{x+4} )=2[/tex]
By using the definition of a logarithm we can say that:
[tex]\frac{x-6}{x+4} = 6^{2}\\\frac{x-6}{x+4} = 36\\x -6 = 36x+144\\35x = -150\\x =-\frac{30}{7}[/tex]
When plugging this solution in, you find that the term [tex]log_{6}(x-6)[/tex] has x-6 evaluate to a number less than 0. This is not included in the domain of log functions, so [tex]-\frac{30}{7}[/tex] is not a valid solution. This means that there are no solutions.
