Power Law of Logarithm

Morning people! Today, I'll be continue my advanced function blog with Power Law of Logarithm. Frankly, I think this is rather an easy logarithm law. I hope you guys will be having an easy time to understand, ingest and digest the knowledge I share today! :)


log_bxⁿ = nlog_bx


for example: log(x^-1) = -log(x)
                    log(x²) = 2log(x)


----------------------------------------------------------------------------------


Usually when we do logarithm exercises, we will encounter logarithmic equations or functions that have base other than 10. For instance, 2, 9, x, 0.5.... bla, bla, bla...


So, what we can do here is that to express the logarithmic function or equation using the change of base formula.


For example, log_bm how are we going to evaluate it?

1. Make "log m" as the upper portion of a division.
2. Make "log b" as the lower portion of a division.
3. Combine both "log m" and "log b" into "log m / log b".
4. Now you can evaluate the answer using calculator or manually.


In conclusion, i scan the text book and I have the key concept of Power Law of Logarithm for you. 

For more exercises and information, please go to this link. Click me!!! :)

Watch this video!!! I love the way he explains how to change the base of logarithm! Clean and clear！ 

Source: PatrickJMT, Youtube 2011.
             The Math Page "Topic in Precalculus"