Download (4 3)⋅ 243 81 ÷ logb y x = log 17 x = log 81 x log 8 log 6 +

6.1 Exponential functions
1. Write the general form of an exponential function.
2. Write 3 examples of exponential functions
3. Draw the graph in exercise #1
6.2 Positive Integer Exponents
1. For positive integers n, clearly explain what xn
means? Give two examples.
2. Read the agreement on page 232 and write 3
examples to illustrate the agreement.
3. Are (2x)3 and 2x3 different, explain.
2
Example 1. Evaluate 4 ⋅ 32 and (4 ⋅ 3)
Example 2. Evaluate (-3)3 and -33
Example 3: Evaluate 65 by multiplying by hand, and
then confirm using a calculator.
6.3 Properties of Exponentiation
1. For each property on page 237, give an example with
numbers to show how it works.
Example 1. Simplify (3x3y5)2(4x6)
Example 2. Show by evaluating numerator and
denominator with a calculator that 412/44 = 48
6.4 Rational Exponents
1. Give two examples of the rule for negative
exponents. Explain how this rule makes sense.
2. Give two examples of the rule for 0 exponents.
Explain how this rule makes sense (hint use the division
of powers rule)
4. Give two examples of the rule for reciprocal
exponents. Explain how this rule makes sense (Hint:
use the multiplication of powers rule)
5. Give 2 examples of the rule for fractional exponents.
Explain how this rule makes sense (Hint: use the
multiplication of powers rule and the reciprocal
exponents rule)
Example 1. Show that 1222/3 is the same as (1221/3)2 Do
both with a calculator which will take roots.
Example 2. Approximate 4 256.57 using only the
square root button of a calculator. (Don’t use a 4th root)
Example 3. Simplify
2
3
(4 x y −6 z 2 ) 4
12 x 3 y 4 z −2
6.5 Powers of Radicals w/o Calculators
Example 1. Evaluate 2563/4
Example 2. Evaluate 17285/3
Example 3. 5 243 ÷ 3 81
6.6 Scientific Notation
1. Write a number in scientific notation and label the
mantissa and characteristic.
2. What is the range of possible numbers for the
mantissa?
Example 1: Write in scientific notation
a. 4566839205867
b. 0.000000034567
Example 2: Multiply (4x1012) (6x10-22)
Write the answer in scientific notation
6.8 Solving by Logarithms
1. Give two examples of a base 10 log.
Example 1. Solve and check 10x=372
Example 2. 34x10-0.3x=59
Example 3. Solve and check 7x= 271
6.9 Logarithms with other bases
1. Give two examples of a log with a base other than 10
2. Write the names of y, b, and x in the following
equation y = log b x
Example 1. Find x if log 5 x = 17
Example 2. Find x if log 6 81 = x log381=
4
Example 3. Find x if log x 7 =
5
6.10 Properties of Logarithms
1. Give examples of all of the properties on page 276.
Example 1: Given that log 2 ≈ 0.301 and log 3 ≈
0.477, find an approximation for the log of 108 without
using a calculator log key.
Example 2: Express log12 8 + log12 6 as a single
logarithm of a single argument.
Example 3: Solve 6x=92 by taking the log of each
member and using the log of a power property.
6.11 Proofs of Log Properties
Example 1: Find a decimal approximation for log338
Example 2: Prove that
logb(x/y) =logbx - logby
6.12 Inverses of Functions
1. Give an example of a function and its inverse.
2. What is the standard notation for the inverse of a
function?
3. What is the most striking feature of a function and
its inverse?
Example 1: If f(x) = 6x+4.5 sketch the function and
its inverse and tell whether the inverse is a function.
Example 2: Invert f(x) = x2+3x-4 and sketch the two
graphs. Is the inverse a function?
6.13 Add-Multiply Property of Exponential
Functions
1. Prove the add-multiply property of exponential
functions.
2. Prove the add-add property of linear functions.
Example 1: Suppose that f(x) varies exponentially with
x and f(2)=300 and f(6) = 200. Calculate values of f(x)
and use the information to draw the graph.
Example 2: Which of the following functions f or g
could be an exponential function and why is the other
one not an exponential function?
x
f(x)
g(x)
2
76.4
93.1
5
62.7
76.405
8
51.457 58.773
11
42.23 44.525
If the domain of this function is 0<x<20, what is f(7)
6.14 Mathematical Models
1. Write the standard forms for these equations: linear,
quadratic, and exponential, variation (direct and
inverse) and logarithmic.
Example 1: Problem 1 page 303.