Thursday, 12 November 2009

There are several important announcements:

1. Test 4 is on Tuesday, 24 November 2009 and will cover at least Sections 2.6, 3.1, 3.2, 3.5, 3.6, 4.1, 4.2, 4.3 and, maybe 4.4;
2. Homework will not be collected next week;
3. There will be a quiz Tuesday (on Section 4.1) and a quiz on Thursday.

Today, we discussed Section 4.1 (exponential functions) and started Section 4.2 (logarithmic functions). Remember that the logarithm function is the inverse function of exponential functions. You should refresh your memory about transformations of functions, domain and range of functions, intervals of increase/decrease

The following definition of logarithm is extremely important:

y = log_b(x) <=> x = b^y

Also, there are some properties of logarithms that we will discuss on Tuesday. You may want to start memorizing them now. Here they are:

1. log_a(1) = 0
2. log_a(a) = 1
3. log_a(a^x) = x and a^log_a(x) = x
4. If log_a(x) = log_a(y), then x = y
5. log_a(x) = log_b(x)/log_b(a)
6. log_a(u*v) = log_a(u) + log_a(v)
7. log_a(u/v) = log_a(u) – log_a(v)
8. log_a(uⁿ) = n*log_a(u)

Homework for Sections 3.5, 3.6 and 4.1 will not be collected but you should be familiar with the questions:

• Section 3.5: #7-17, 23–26, 31, 33, 35, 37, 39
• Section 3.6: #1, 2, 6, 9–25, 27–30, 32, 33, 34, 36, 59–62, 65–68
• Section 4.1: #1–22, 27-36, 51-52

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