Unit #6 Introduction to Exponential and Logarithmic Functions Review
1
2
1) If x is a positive integer, 4 x is equivalent to
2) The expression
(1)
2
(2) 4 x
x
(3) 2 x
(4) 4
1
x
(3a 4b3 ) 2
is equivalent to:
3a 5b6
a. 3a 3
c.
b. 3a13
d.
a9
a
b
3) Which of the following is equivalent to y  4 x ?
a. y  log 4 x
b. x  log 4 y
c. y  log x 4
d. x  log y 4
4) Which of the following is the inverse of y  4 x
a. y  log 4 x
b. x  log 4 y
c. y  log x 4
d. x  log y 4
5) What is the y-intercept of y  log3 (2 x  1)  8 ?
a.
1
2
b. -8
c. 4
6) Which of the following is not in the domain of y  log 2 (4 x  6) ?
a. 1
b. 2
c. 3
7) Write the expression
 
6
8
x in simplest exponential form.
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d. there is no y-intercept
d. 4
8) Evaluate the following logarithms. If needed, write an equivalent exponential equation. Try as many as
possible without the use of a calculator.
a. y  log 2 32
b. log 27 3
 1 
c. log 5 

 625 
d. y  log 4 64
e. log 10,000
f. log √100
g. ln e
h. ln e7
𝑛4
3
j. 𝑙𝑜𝑔7 √343
i. log 1
k. 𝑙𝑜𝑔𝑛 ( )
𝑛
9) Between what two integers must the value of log5 250 lie? Justify your answer.
10) Use the properties of rational exponents to determine the value of y for the equation,
4
5
 
x 
   xy
5 7
x
3
2
11) Solve for x:
.
6 x1 
1
36
2
4
l. 𝑙𝑜𝑔9 (√81)
12) Evaluate and show your work:
27

2
3
=
13) What point lies on every exponential function in the form y  b x where b>0 and b  1. Why is this point
on every graph?
14) What point lies on every logarithmic function in the form y  logb x where b>0 and b  1. Why is this
point on every graph?
1
6 2
 36 x y 
4 x 5x y 
4
15) Express the following in simplest form:
3
4
3
16) Simplify each of the following problems. You must show your work.
48x11 y 6
a)
c)
3
b)
81x9 y14
3
3
27x 6 y 9
17) Two exponential functions, f ( x)  ab x and g ( x)  cd x are graphed in each row of the table. Finish the
rest of the table by identifying and explaining the relationship between a and c as well as the relationship
between b, 1, and d.
Graph
18) Solve for x:
Relationship between a and c.
Explain
272 x1  94 x
4
Relationship between, b, 1, and d.
Explain.
19) Given the function y = 3x
a. Graph y = 3x and its inverse on the grid below. Please show a table of values for each function.
y
b. Show the algebraic process for finding the inverse of y = 3x
x
c. State the domain and range of y = 3x using interval notation.
d. State the domain and range of its inverse using interval notation.
20) Simplify the following expression. Express your answer in simplest exponential form and in simplest
radical form.
6
3
4x  x
2
3


 256 x 


8
3
3
4
2
 125  3
21) Evaluate and show your work: 
 =
 8 
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