A Log Questions for ya

1. Dec 10, 2005

MajikWaffle

http://img228.imageshack.us/img228/1799/untitled8av.png [Broken]

Kinda Tricky

Last edited by a moderator: May 2, 2017
2. Dec 11, 2005

Tide

Not too tricky - it's just the Golden Ratio.

3. Dec 11, 2005

JasonRox

A nice little question.

I'll give a hint.

9*16=144

12*12=144

Last edited by a moderator: May 2, 2017
4. Dec 12, 2005

MajikWaffle

Yar, still can't get it. Answer anybody

5. Dec 13, 2005

Tide

The answer is in #2 above.

6. Dec 10, 2010

Avodyne

The problem is to find $a/b$ given
$$\log_9 a = \log_{12}b = \log_{16}(a+b)$$

Let $$x = \log_9 a = \log_{12}b = \log_{16}(a+b)$$. Then

$$a=9^x,~~~b=12^x,~~~a+b=16^x$$

Now, compare $a(a+b)$ with $b^2$.

7. Dec 10, 2010

Staff: Mentor

We do not give out answers here at the PF. Show some effort, or your thread will be deleted.