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Logarithms in a nutshell

Someone asked me recently to make a post about logarithms. So here goes. I already answered the person in an email but I thought I could include some interesting history tidbits here, too.

Logarithms are simply the opposite operation of exponentation.

For example, from 23 = 8 we get log28 = 3, and we read it "base 2 logarithm of 8 equals 3".

So it's not difficult: if you understand how exponents work, logarithms have the same numbers, just in a little different places.

Just as in exponentiation, a logarithm has a base (2 in the above example). Remember that in 53, 5 is called the base and 3 is the exponent.

Other examples:
53 = 125 and log5125 = 3.
104 = 10,000 and log1010,000 = 4.
2x = 345 and log2345 = x.

As you can see from the last example above, you can use logarithms to solve equations where the x is the exponent:
4x = 1001
x = log41001.

Then you'd get the value of x from a calculator.

However, the base of the logarithm can be anything and most calculators only have two bu…
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Saxon Math is not for everyone

(Updated in 2018)

People sometimes ask me of my opinion or review of Saxon math. What I've written here applies in particular to Saxon Math's high school courses and middle grade levels. (The grades K-3 are by a different author and are quite different; more on that below.)

Saxon Math uses an "incremental approach" where math concepts are studied in little pieces over several lessons, and those lessons are strawed over a long period of time, intermixed with lessons about other topics.

In other words, if one lesson is on some particular topic (say, percentages or inequalities), it's almost guaranteed that the NEXT lesson is NOT on that topic. It jumps around from topic to topic constantly, and this is by design.

Saxon's method also includes a feature where after a lesson is taught, there are very few practice problems about the topic of the lesson. Most of the problems are mixed review problems, and they practice concepts from earlier lessons, not the concept …
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