Log Law: Change Base Explained w/Example

[dilan]

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

 

[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?

 

[tacman]

in advance!

Hi there, no problem! The log law of change base states that if we have a logarithm with base a, we can rewrite it as a logarithm with base b by using the following formula:

log base a (x) = log base b (x) / log base b (a)

Let's say we have the logarithm log base 2 (8). We can rewrite this using the change base formula as:

log base 2 (8) = log base 10 (8) / log base 10 (2)

Now, we can easily solve this using our calculator to get log base 2 (8) = 3.

I hope this example helps clarify the log law of change base for you! Let me know if you have any other questions.