SOLUTION: Please help me solve the inequality Log4(2-x) > log2x. thank you for your attention.

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Question 982516: Please help me solve the inequality Log4(2-x) > log2x.
thank you for your attention.

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Since the log function increases as x increase, you can just solve for the argument inequality.
4%282-x%29%3E2x
8-4x%3E2x
8%3E6x
x%3C8%2F6
x%3C4%2F3
An additional requirement is that both arguments remain positive since log function can only have positive arguments.
4%282-x%29%3E0
2-x%3E0
x%3C2
and
2x%3E0
x%3E0
So all three of these requirements must be met simultaneously leading to,
0%3Cx%3C4%2F3