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Alg2 lesson 10-4 and 10-5
1.
A common logarithm
has a base of 10. log 5 means log10 5 The log key on your calculator will find common logs.
2.
Solve Example 4-3a
3.
Solve log 3x
= log 17 x log 3 = log 17 x = log 17log 3 1.23040.4771 = = 2.5789 Example 4-3c
4.
Solve:
5.
Solve: 5x
+ 3 = 2x+4 log 5x + 3 = log 2x+4 (x + 3) log 5 = (x + 4) log 2 x log 5 + 3 log 5 = x log 2 + 4 log 2 x log 5 – x log 2 = 4 log 2 – 3 log 5 x(log 5 – log 2) = 4 log 2 – 3 log 5 x = 4 log 2 – 3 log 5 log 5 – log 2 = 4(0.3010) – 3(0.6990) 0.6990 – 0.3010 = -2.244
6.
Change of base
formula
7.
Find Example
4-5a
8.
Find Example 4-5b
9.
Quantities that grow
or decay continuously can be described by a natural exponential function. f(x) = ex e is a constant e is approximately 2.71828
10.
Use a calculator
to evaluate each expression to four decimal places. a. b. Answer:1.3499 Answer:0.1353 Example 5-1c
11.
The inverse of
the natural exponential function is the natural log function. y = ex loge x = y loge is usually written as ln
12.
Use a calculator
to evaluate each expression to four decimal places. a. In 2 b. In Answer:0.6931 Answer:–0.6931 Example 5-2f
13.
Write
as a natural logarithmic equation. x = loge23 x = ln23 Example 5-3a
14.
Write
as an exponentialequation. loge x = 2.25 Example 5-3c
15.
Evaluate Evaluate Evaluate
Answer: Answer: Answer: Example 5-4a
16.
Solve loge
2x = 0.7 2x = e0.7 x = ½ e0.7 Answer: about 1.0069 Example 5-7d
17.
Solve Example
5-5a