# Log law -Change base

1. Jan 25, 2006

### dilan

Hi,
I am just a little confused with this log law of change base. Is there any one who can give me a clear description with an example?
Thanks

2. Jan 25, 2006

### arildno

Let a,b>0, and distinct from 1 be the respective bases, and let c be an arbitrary positive number.

Then, you evidently have:
$$c=a^{log_{a}(c)}=b^{log_{b}(c)$$
Taking the logarithm with respect to a on both sides, you get:
$$\log_{a}(c)=\log_{b}(c)\log_{a}(b)$$
that is:
$$log_{b}(c)=\frac{log_{a}(c)}{log_{a}(b)}$$
Was that what you're after?