Solve the following logarithm below:

Question

log_6 (-5r - 2) = log_6 ( r - 4)

there is no solution to this correct?

Answer 1

If log_6 (-5r - 2) = log_6 ( r - 4) , then
-5r-2 = r-4
-6r = -2
r = 1/3

but then -5r-2 = -11/3 and r-4 = -11/

and since we cannot take log of a negative, there is no solution.