# Complete Logarithmic forumlas

#### MrAnderson

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
Gold Member
Here ya go...

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

$y=a^x$ if and only if $log_a(y)=x$

Next we have:

$\log_b(xy)=\log_b(x)+\log_b(y)$
$\log_b\left(\frac{x}{y}\right)=\log_b(x)-\log_b(y)$

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:

$\log_b\left(a^x\right)=x\log_b(a)$

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

$\log_b\left(b^x\right)=x\log_b(b)=x$

The last step is justified because $\log_b(b)=1$.

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

$$\log_a(x)=\frac{\log_b(x)}{\log_b(a)}$$

#### MrAnderson

Thanks for the post and for the explanation. :)

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