Solving for x: log 3 (x^2 -5x+6) - log 2 (2-x) = 2

[JoanF]

Homework Statement

Find x:

log 3 (x^2 -5x+6) - log 2 (2-x) = 2

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]

Homework Statement

Find x:

log 3 (x^2 -5x+6) - log 2 (2-x) = 2

Some clarification, please. Is this
log[3(x² - 5x + 6)] - log[2(2 - x)] = 2

or
log₃(x² - 5x + 6) - log₂(2 -x) = 2
?

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 ...

 

[JoanF]

Some clarification, please. Is this
log[3(x² - 5x + 6)] - log[2(2 - x)] = 2

or
log₃(x² - 5x + 6) - log₂(2 -x) = 2
?

it is log₃(x² - 5x + 6) - log₂(2 -x) = 2

 

[Mark44]

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)

 

[JoanF]

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)

You got the same I got


Yes I'm sure ...