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#### The Algebra Index

Algebra It's extremely scoring once you understand the basic concepts. Just start by reading up the series of lessons below! Basics of Algebra: Part I Basics of Algebra: Part II Basics of Algebra:...

**The
Logarithms**

Introducing-
logsLogarithms, which we'll refer to
as logs, are an important mathematical concept. Logs are very
simply a way to represent a mathematical relation. They're a lot
loss scary than you may think. No reason to freak out.Let's go over basic stuff- how can I represent the number 4? Well, there are infinitely many ways to do so. is one way. is another. So is , and . And so is . |

Oh no! Freak out!
Ahh!No, that's a joke. See, logs are just one more way to say 4, or 20, or other numbers. In that case, you may think logs are useless. Well, let's look at the formal definition: If , then . So for example, we all know that . Thus, . See, it really is simple! So and . % %{font-family:verdana;font-size:13px}Logs are super useful when you want to know something like this- for what x will ? That's simple, for , which you can find out using a scientific calculator. The answer will be something like 9.22. So you see, logs are really useful in some situations. |

**Log rules!
(literally)**

There are a few important log rules you should know:

1. , which makes sense because .

2. . This is because .

3. .

4. (most useful rule!)

5. (change of base formula).

The change of base formula is
extra-useful because calculators usually give only results (generally speaking, log with no base
specified is taken as log base 10). Also, note the domain of the inside of the log. If we have , then . This makes intuitive sense looking at the basic definition of the log. |

**Let's do some
practice!**

Ex: Solve for x, if .

Super easy! Let's first use rule 3. We have: . Notice that by cube laws, , so we're left with .

Now, apply the general log principle. What this really means is that , so we continue solving and find that or .

Finally, we note that since is undefined, x can't be -5. So our answer is !

Logs are fun! |

That's pretty much all you need to know. You can practice some simple log problems on the log test. Good luck!

**That's it for
logs!**

Photo
Credits:

Back on the Log Train, by Claire L. Evans, Standing on logs may be dangerous by pfly, Logging truck by pingnews.com, Logs Vancouver by ahisgett

For an excellent discussion on logarithms, please click on:

www.math-for-all-grades.com

Thanks a lot ,,,,

I was so confused about these all but now i think i can go ahead
with this slogans and all ,,

:))

But Maths Sucks :((

Basics of Algebra: Part I

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