# Finding log something, in terms of A and B.

1. Oct 19, 2009

### Suy

1. The problem statement, all variables and given/known data

If Logb2=A and Logb49=B, what is logb397, in terms of A and B.

This is one of the bonus question in my geometric quiz and i don't remember if the number is 397. I wonder if anyone get this?
2. Relevant equations

3. The attempt at a solution
here is what i did
bA=2 and bB=49
b=21/A b=491/B
491/B=21/A --> log(49)/log(2)=B/A

because this is geometric quiz, so i assume this one have a geometric
so i use arn-1
r : log(49)/log(2)=B/A
a : Logb2

Logb2(B/A)n-1=logb397
am i right?
ty!

2. Oct 19, 2009

### Staff: Mentor

I'm guessing that the number is 392, not 397. 392 = 8*49 = 23*49.
This makes no sense whatever. From your presentation of the problem, it has nothing to do with a geometric sequence, or anything else having to do with geometry. This problem is strictly concerned with the properties of logarithms.
I'm assuming that this is the actual problem description:
If Logb2=A and Logb49=B, what is logb392, in terms of A and B.​

logb 392 = logb (8 * 49) = logb (23 * 49)

Now, use the properties of logs on the last expression above to get quantities that are in terms of A and B.

3. Oct 19, 2009

### Suy

but i remember it is a odd number

4. Oct 19, 2009

### Staff: Mentor

Well, if you can't remember exactly what the problem is, I can't help you.

5. Oct 19, 2009

### Suy

but what happen when it is a odd number? like 397, is it possible to solve it?

6. Oct 19, 2009

### Staff: Mentor

If you don't know what the number is, you can't work the problem - that's what happens.

7. Oct 19, 2009

ok, thx