1. ## Quick LOG question!

How do I go about solving this? I know the log rules, I just can't figure it out.

Question:

log4(x+2) + log4(x-3) = log(4)9

THE "4" IN EACH TERM IS THE BASE. NOT LOG 4, LOG BASE 4.

2. Originally Posted by Jeavus
How do I go about solving this? I know the log rules, I just can't figure it out.

Question:

log4(x+2) + log4(x-3) = log(4)9

THE "4" IN EACH TERM IS THE BASE. NOT LOG 4, LOG BASE 4.
recall:
$\log_a x + \log_a y = \log_a (xy)$

so combine the left hand side using that formula, then equate the things that are being logged on both sides.

3. Yeah, I know the rules. I've done that, and I'm not getting the correct answer. =/

4. Originally Posted by Jeavus
Yeah, I know the rules. I've done that, and I'm not getting the correct answer. =/
$\log_4 (x + 2) + \log_4 (x - 3) = \log_4 9$

$\Rightarrow \log_4 [(x + 2)(x - 3)] = \log_4 9$

$\Rightarrow (x + 2)(x - 3) = 9$

5. Ahh, thank you.

I didn't think it'd go as far as having to use the quadratic equation.

6. Originally Posted by Jeavus
Ahh, thank you.

I didn't think it'd go as far as having to use the quadratic equation.
i'm curious as to what you did after you apply the rule. but never mind