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)
To solve for x, we must first combine the logarithms using the quotient rule: log3((x2 - 5x + 6)/(2-x)) = 2. Then, we can rewrite the equation as 32 = (x2 - 5x + 6)/(2-x). From there, we can solve for x using algebraic methods.
The domain of this equation is all real numbers except x = 2 and x = 3, since those values would make the logarithms undefined.
Yes, this equation can be solved using a calculator by converting the logarithms to exponential form and using the inverse function on the calculator.
Yes, this equation can also be solved by graphing the two sides of the equation and finding the points of intersection. However, this method may not give an exact solution.
The possible solutions for this equation are x = 1 and x = 6. These are the values that make the left and right sides of the equation equal.