# 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?