Solve Log Equation for x: 2log3x + log3(x-1) = log32 + log36x | Homework Help

[chops369]

Homework Statement

Solve for x:
2log₃x + log₃(x-1) = log₃2 + log₃6x

Homework Equations

N/A

The Attempt at a Solution

Ok, so I tried to solve it and I came up with this and got stuck.

log₃(x³-x²) = log₃12x
Even if I canceled out the logs it would be x³-x² = 12x and then how would I solve?

 

[tiny-tim]

Welcome to PF!

Hi chops369! Welcome to PF!

Solve for x:
2log₃x + log₃(x-1) = log₃2 + log₃6x
…
log₃(x³-x²) = log₃12x
Even if I canceled out the logs it would be x³-x² = 12x and then how would I solve?

Divide both sides by x.

 

[chops369]

Ohhhh, I see now. I didn't know you had to factor. Thanks a lot.

 

[romolo]

Careful of dividing by x! It's OK in this problem since x=0 is an extraneous solution, but you do run the risk of losing a solution.

 

[Дьявол]

It is better if you factor x:
x³-x²-12x=0

x(x²-x-12)=0

One of the solutions is x₁=0

The other two come from the quadratic equation.

As you can see zero, can't be solution because if you put the 0 in the first equation, it would not be possible since log₃0 doesn't exist.

Regards.