Question 1090402: Logbase6 (x-5)-logbase6x=2
Answer by greenestamps(13203)   (Show Source):
You can put this solution on YOUR website!
The equation is
log_6(x-5) - log_6(x) = 2
This is equivalent to
log_6((x-5)/x) = 2
The expression on the left in the equation is only defined for values of x greater than 5. And for all values of x greater than 5, (x-5)/x is a number less than 1. That means the logarithm base 6 of (x-5)/x is going to be negative; it will never have the value 2.
Algebraically, we make the right side into an expression using log base 6 and try to solve:
log_6(x-5) - log_6(x) = 2
log_6(x-5) - log_6(x) = log_6(36)
(x-5)/x = 36
x-5 = 36x
-5 = 35x
x = -1/7
But the expression is not defined for this value of x.
The only algebraic solution is invalid; so there is no solution to the equation.
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