## Solving Log functions... x + 7 / x - 9 = 11

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.
Merz
Posts: 1
Joined: Mon Feb 23, 2009 4:27 pm
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### Solving Log functions... x + 7 / x - 9 = 11

I forgot some of my algebra and can't recall what to do with x+7/x-9=11...

nearly done.

DAiv
Posts: 36
Joined: Tue Dec 16, 2008 7:47 pm
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### Re: Solving Log functions...

Hi Merz, welcome to the forums.

As written, the equation you gave was $x \,+\, \frac7x \,-\, 9 \,=\, 11$, which I presume you meant rather than $\frac{x \,+\, 7}{x \,-\, 9} \,=\, 11$, (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.)

Solve for $x$:

$x \,+\, \frac7x \,-\, 9 \,=\, 11$

$x \,+\, \frac7x \,-\, 9 \,+\, 9 \,=\, 11 \,+\, 9$

$x \,+\, \frac7x \,=\, 20$

Get rid of the fraction on the left hand side by multiplying both sides by $x$:

$x \, (x \,+\, \frac7x) \,=\, 20x$

... and multiplying out the parentheses:

$x^2 \,+\, 7 \,=\, 20x$

Bring the $20x$ over and rearrange:

$x^2 \,-\, 20x \,+\, 7 \,=\, 0$

And now you're left with a quadratic equation.

Can you continue from there?

DAiv