# Last log Question I Promise!

• Jun 29th 2008, 09:08 PM
karleewil
Last log Question I Promise!
Log(x-46)+log(x-61)=2

thank you
I love you all!!
• Jun 29th 2008, 09:23 PM
Jhevon
Quote:

Originally Posted by karleewil
Log(x-46)+log(x-61)=2

thank you
I love you all!!

i suppose we are working in base 10 for the logarithm

$\displaystyle \log (x - 46) + \log (x - 61) = 2$

$\displaystyle \Rightarrow \log [(x - 46)(x - 61)] = 2$ ..............since $\displaystyle \log_a X + \log_a Y = \log_a XY$

$\displaystyle \Rightarrow (x - 46)(x - 61) = 10^2$ ...............since $\displaystyle \log_a b = c \implies a^c = b$

this is a quadratic, i hope you can take it from here

this is essentially the same as the question you asked here, what did you not understand?
• Jun 29th 2008, 09:51 PM
karleewil
yeah well
the factoring part thats where i have trouble

what multiplied by what equals 2706 with 107 in between?
• Jun 29th 2008, 09:56 PM
Jhevon
Quote:

Originally Posted by karleewil
the factoring part thats where i have trouble

what multiplied by what equals 2706 with 107 in between?

if you have trouble factoring large numbers, you can always use the quadratic formula

to solve $\displaystyle ax^2 + bx + c = 0$ you use the formula $\displaystyle x = \frac {-b \pm \sqrt{b^2 - 4ac}}{2a}$

you have $\displaystyle x^2 - 107x + 2706 = 0$, if you want to factor this, you must come up with two numbers that when multiplied gives you 2706 and when added gives you -107.
• Jun 29th 2008, 09:58 PM
karleewil
hmm...
yea I know I just said that if you recall.
• Jun 29th 2008, 10:48 PM
mr fantastic
Quote:

Originally Posted by karleewil
yea I know I just said that if you recall.

0. To me, this reply (to someone who has actually just given you exactly the help you require) is very close to being insulting. Try reading the reply again and thinking about what it says.

1. If there's a particular part of a question that you're stuck on, you should state in the initial post what the question is (which you did) and where you're stuck.

Otherwise people waste time including in their reply things that you've already done.

2. Your problem is solving quadratic equations. You're struggling to solve by factorsing. So Jhevon gave you the quadratic formula which can always be used to solve a quadratic equation.

I doubt you would be given these sorts of questions to solve if you hadn't been taught how to solve quadratic equations. Try using the formula. Post where you get stuck (if you get stuck).

3. Given that solving quadratic equations is an obvious weakness, I'd suggest you thoroughly revise it in your textbook or class notes.