Welcome. This is Section 4.4 Evaluating Logarithms and the Change of Base Theorem.
Two of the most important bases for logarithms are 10 and e.
Let's start with 10.
For all positive numbers x, log x equals log of x base 10. We say that a base 10 log is a common log.
Our calculators have a common log key.
The common log key just says log.
I'm going to open a calculator on screen here and try some.
Here is a TI-84 and pressing log key shows that on the display and opens up a parentheses.
Try something like the log of 10,000. And we place the 10,000 inside the parentheses and hit enter.
The answer returned by the calculator is 4.  So the common log of 10,000 is 4.
Suppose we take the common log of 341.
This time we end up with a number a little more that 2 1/2 that is 2.53 ... .
We'll do one more.  Press the common log key and plug in 0.06891.
Here we see the common log is about -1.16 and so forth.
Continue on the next page.  These are answers that we got. And I'll drag the calculator answers onto our screen.
