5.4

Hello everyone!

So as far as five four goes, it’s just building off of five three’s ideas. To start it all off, let’s review:

Last section told us that log has a subscript 10 (common log) and that ln has a subscript e (natural log). Now that we have that covered, moving onto the…

Law of Logarithms.

1) log_a(uw) = log_au + log_aw

2)log_a(u/w) = log_au - log_aw

3)log_a(u^c) = c log_au

Easy enough, right? Now to le comparisons.

Common Logarithms	Natural Logarithms
log(uw) = logu + logw	ln(uw) = lnu + lnw
log(u/w) = logu – logw	ln(u/w) = lnu – lnw
log(uc) = c logu	Ln(uc) = c lnu

There are no differences in the way you play out these logarithms, just differences in the meanings.

BUT, BEWARE. THERE IS A SLIGHT CATCH. Log_a(u+w) does NOT translate to log_au + log_aw. Also, log_a(u-w) does NOT translate to log_au – log_aw. This isn’t like f(x) in those ways at all!

     ^ You can’t have a log of a negative number, that’s why -4 doesn’t work.

Onward again, 

So I think that’s about it, I hope this helped!

Have a great weekend!

P.s. COME TO FALL PLAY TOMORROW AT 2 PM. MR WILHELM WENT TONIGHT(sorry I didn't say hi to you) SO YOU SHOULD GO TOMORROW.

Kristy :]

Section 5.3 - Logarithms!

This section was on logarithms! Logarithms are basically the inverse of an exponential equation. Literally, it means ratios of numbers.

exponentiation is what is being done to X in this case.


To solve, we need to undo what is being done to X, which is a logarithm :)

Mr. Wilhelm's KEY TO EVERYTHING!

That is how to rewrite an exponential function as a logarithmic function. With this, we can solve exponential equations that would otherwise be unsolvable!

This is how you might apply a logarithm to an exponential function. As you can see, Y=1,000  A=10   and X=3

The key to everything is as easy as that :)

Special Logarithms!

When it is just written "log" with no subscript, it is implied that it is log10 -- COMMON LOG!

When it is written ln, it is implied that it is loge -- NATURAL LOG!

How to graph a logarithm!

A few other little tidbits to know:

since the domain of an exponential function is (-∞, ∞), so thats the RANGE of a logarithm

the range of an exponent is (0, ∞), so thats the DOMAIN of a logarithm. (unless it has been moved by the C value)

*Exponents and Logarithms are 1 to 1*

Sorry, there are no pretty logarithm pictures on the internet :(

Links and stuff:

http://www.themathpage.com/aprecalc/logarithms.htm

http://www.sosmath.com/algebra/logs/log1/log1.html

http://www.purplemath.com/modules/logs.htm

http://www.shodor.org/unchem/math/logs/index.html

http://www.youtube.com/watch?v=mQTWzLpCcW0

And, just for old time's sake :

Nonagon Song - http://www.youtube.com/watch?v=x5ohtlewREI

One Dozen Monkeys -http://www.youtube.com/watch?v=2qdql9vsWWM&feature=related

Hope this helped and made logarithms a little less unbearable :)

Bye, Katie