Hi Merz, welcome to the forums.
As written, the equation you gave was
, which I presume you meant rather than
, (x+7) / (x-9) = 11. In either case, you don't need logs to solve these.
So, assuming you did mean the first version, I'll take you part way and give you a pointer for the rest. (If you didn't mean that version, let me know and I'll post a reply for the other one.)
Add 9 to both sides:
Get rid of the fraction on the left hand side by multiplying both sides by
... and multiplying out the parentheses:
over and rearrange:
And now you're left with a quadratic equation.
Can you continue from there?