Name: __________________
1
Class:
Date: _____________
Evaluate the expression
log
2
1000
Use the properties of logarithms to solve the equation for x.
ln(3x 1) ln(x a. x = 0
3
10
1) = ln8
b. x = 7
5
c. x =
5
7
d. x =
1
5
Solve the equation for x.
log 2 (9 + x) = 5
4
Sketch the graph of the function.
g ( x ) = log ( x 3
1) + 4
Select the correct graph.
5
Determine the values of x that satisfy the expression
(
ln x
PAGE 1
2
+ 3
)
= ln ( x 2 ) + ln ( x + 3 )
e. x =
7
5
Name: __________________
6
2
2 x/2
6
x2
x + 1
3 2
x
= 0
Rewrite the expression as a single logarithm.
ln (x 9
1)
Determine all values of x that satisfy the following equation.
x 4
8
Date: _____________
Use the properties of logarithms to simplify the expression so that the result does not contain logarithms of products, quotients, or
powers. Assume that all necessary conditions are satisfied.
log (8x 7
Class:
1) + 1 ln x 2
5ln x
Rewrite the expression as a single logarithm.
ln x + 2ln (x + 5)
PAGE 2
Name: __________________
Class:
Date: _____________
10 Sketch the graph, showing any horizontal asymptotes.
f( x ) = e
x 2
+ 3
a.
d.
b.
e.
c.
11 Determine the domain of f ( x ) =
PAGE 3
2 3x
x e
xe
3x
2e
3x
.
Name: __________________
Class:
Date: _____________
12 Use the properties of logarithms to simplify the expression so that the result does not contain logarithms of products, quotients, or
powers. Assume that all necessary conditions are satisfied.
ln
x
3
x
4
2
x 1
+ 8x + 16
a. 4ln x 1 ln(x 2
1) + 2 ln(x 3
b. 4ln x +
1 ln(x 2
1) c.
1 ln(x 2
1) 4)
d. 4ln x +
1 ln(x 2
1) 2 ln(x + 4)
3
2 ln(x + 8)
3
e. 5ln x +
1 ln(x 2
1) 2 ln(x + 4)
3
2 ln(x + 4)
3
13 Sketch the graph of f ( x ) = 4 e
x 3
.
Select the correct graph.
14 Evaluate the expression.
lne
1/ 2
a. 2
PAGE 4
b. e
c.
1
2
d. e
1/ 2
e. e
2
Name: __________________
Class:
Date: _____________
15 Evaluate the expression.
log 625 5
16 Determine all values of x that satisfy the following equation.
2
2x 3
= 8
17 Determine all values of x that satisfy the following equation.
3
x 5
= 9
x + 2
18 Find the domain of the function
2
f ( x ) = ln
x x 4
5
19 Use the inverse relationship with the exponential functions to determine x
x = log 64
4
20 Use the properties of logarithms to simplify the expression so that the result does not contain logarithms of products, quotients, or
powers.
ln x (x + 6)
PAGE 5
ANSWER KEY
Exponentials and Logarithms
1. 3
6. 6log2 ( 8x
11. ( 1)
, 1 2, )
16. 3
ANSWER KEY - Page 1
2. e
3. 23
7. 8. ln
1,3
5
x
13. B
12. d
17. ( x 1) x
9
18. ( 2,2 ) ( 5, )
4. D
5. 9
9. lnx ( x+5 ) 2
10. b
14. c
15.
19. 3
1
4
20. ln( x ) +ln( x+6 )