SOLUTION: 1. Solve the equation: logbase4(x-5) = 0.5 – logbase4(1-x). i follow through with the problem and get four different answers but none of them check out when they are plugged int

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: 1. Solve the equation: logbase4(x-5) = 0.5 – logbase4(1-x). i follow through with the problem and get four different answers but none of them check out when they are plugged int      Log On


   



Question 106297: 1. Solve the equation: logbase4(x-5) = 0.5 – logbase4(1-x).
i follow through with the problem and get four different answers but none of them check out when they are plugged into "X".

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Take a step back.
It's tempting to just apply to rules and look for a solution.
For the problem to have a solution, both log arguments (x-5) and (1-x) must be greater than zero
1.%28x-5%29%3E0
2.%281-x%29%3E0
From 1., we get
x%3E5
From 2., we get
x%3C1
You cannot satisfy both condition since there is no x such that
x%3C1 and x%3E5.
No solution.