Steps on how to simplify log5/log125 to 1/3

1. Feb 24, 2005

Gughanath

could someone show me the steps on how to simplify log5/log125 to 1/3. I cant do it :grumpy:

2. Feb 24, 2005

danne89

Which base?

3. Feb 24, 2005

Gughanath

10, sorry for not mentioning that.

4. Feb 24, 2005

dextercioby

It doesn't matter the base,as long it is the same...

Daniel.

5. Feb 24, 2005

Gughanath

yes, so how could I simplify it?

6. Feb 24, 2005

dextercioby

$125=5^{3}$ and use one definitory property of the logarithm...

Daniel.

7. Feb 24, 2005

Gughanath

hmmm....that comes to log5 to the power -2?

8. Feb 24, 2005

danne89

Why don't just: log5 125 = 3 and log5 5 = 1 and then just replace log 5 / log 125 = 1 / 3 ??

9. Feb 24, 2005

dextercioby

No,remember that in general:
$$\frac{\log a}{\log b}\neq \log\frac{a}{b}$$

So pay attention to what u do.
Daniel.

10. Feb 24, 2005

gerben

log(125) = log(53) = 3log(5)

11. Feb 24, 2005

Gughanath

oh right. My bad. so log5/log125 = log5/log5^3 = log5/3log5, the log5's cancel, leaving 1/3. Thanx

12. Feb 24, 2005

danne89

And then cancel out the log(5)s, leaving 1/3?