The problem involves solving the equation log 3 (x^2 - 5x + 6) - log 2 (2 - x) = 2, which includes logarithmic expressions with different bases. The subject area pertains to logarithmic functions and algebraic manipulation.
The discussion is ongoing, with participants clarifying the problem statement and sharing their attempts at manipulation. There is no explicit consensus on the approach, but some productive lines of reasoning have been explored regarding the structure of the equation.
Participants note the complexity introduced by the different logarithmic bases and express concern over the clarity of the problem statement. There is a shared understanding that the equation may require careful handling due to these factors.
Some clarification, please. Is thisJoanF said:Homework Statement
Find x:
log 3 (x^2 -5x+6) - log 2 (2-x) = 2
JoanF said:Homework Equations
The Attempt at a Solution
I tried and got:
(3-x).[(2-x)^1-log 2 (3)] = 9
but I don't know how to get x here ...
Mark44 said:Some clarification, please. Is this
log[3(x2 - 5x + 6)] - log[2(2 - x)] = 2
or
log3(x2 - 5x + 6) - log2(2 -x) = 2
?
Mark44 said:Are you sure you have the problem written correctly? It's very messy with the two log bases. I got to x2 - 5x + 6 = 9(2 - x)(1/log32)