Complete Logarithmic forumlas

1. The problem statement, all variables and given/known data
I need to find as much as a complete logarithmic formulas worksheet or tutorials

I have not been in school for atleast 2 semesters and the class im taking right now makes use of the basic logarithmic functions, not to complicated from what the teacher has told us. I do not remeber anything about logarithms tho so i need to refresh my memory. Im looking for the basic logarithmic formulas(properties) maybe from a website link, a worksheet or a tutorial site online? I appreciate the help.

Tom Mattson

Staff Emeritus
Science Advisor
Gold Member
Here ya go...

The most basic formula is the equivalence between exponental and logarithmic equations:

[itex]y=a^x[/itex] if and only if [itex]log_a(y)=x[/itex]

Next we have:


Verbally these say that the log of a product is equal to the sum of the logs of the factors, and that the log of a quotient equals the difference of the logs of the numerator and denominator.

There is also:


This says that a power inside of a log can be brought out front as a coefficient. A special case of this is when [itex]a=b[/itex]:


The last step is justified because [itex]\log_b(b)=1[/itex].

Finally we have the so-called "change of base" formula:

Thanks for the post and for the explanation. :)

The Physics Forums Way

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving