SOLUTION: Please Help. I found this question on this site, but the wrong answer was given. I need help with the steps. Please~ Solve - log₆x = 1 - log₆(x-5)

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Please Help. I found this question on this site, but the wrong answer was given. I need help with the steps. Please~ Solve - log₆x = 1 - log₆(x-5)      Log On


   

Question 831804: Please Help. I found this question on this site, but the wrong answer was given. I need help with the steps. Please~
Solve - log₆x = 1 - log₆(x-5)
Found 2 solutions by Fombitz, rothauserc:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Duplicate question.
See Answer 500607

Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
note that log base 6 (6) = 1, therefore we have
log base 6 (x) = log base 6 (6) - log base 6 (x-5)
log base 6 (x) = log base6 (6 /(x-5))
x = 6 / (x -5)
x^2 -5x = 6
x^2 -5x - 6 = 0
(x-6)*(x+1) = 0
x = 6 or -1
we can eliminate x = -1 since the log of a negative number is not defined
check the answer
log base 6 (6) = log base 6 (6) - log base 6 (6-5)
1 = 1 - 0
1 = 1
our answer checks :-)