Accelerated Precalculus
Test Exponents and Logarithms
Name ______________________
mini-calculators okay
1. Intuition and Properties involving Logarithms
a. Evaluate each of the following logarithms.
log3 81 _______
log 2 (1/ 8) _______
log 6 1 _______
b. For each of the following expressions, estimate the size of the quantity between the two
closest integers. For example, for the value of π you’d say between 3 and 4. Then, circle the
integer that is closer to the true value. For example, for the value of π you would circle 3.
log12 20
log12 4
log 5 150 between ____ and _____
log 6 82 17
log 6 82 2
between ____ and _____
between ____ and _____
log 3 (1/ 30) between ____ and _____
c. For each of the tables below, fill in the missing values wherever possible. If a value cannot
be determined from the given information, put an X in that blank.
x
log 5 x
1/125
12/25
−1
1
5
12
1.544
d. Express t in terms of base 10 logarithms.
2  3t  10
32t 1  20
144/5
3.544
2. Intuition and Properties involving Exponents.
a. Evaluate each of the following powers. Leave no negative exponents in your answer.
8

4
3
 2ab 4 c3d 0 
 5 4 3 2 
 3a b c d 
_______
x2
2y
_______
3x  6
xy 3
3
_______
b. Write each of the following expressions as a single power such that the only exponent is
‘x’.
2 x 3x
8x
__________
4 x 2
_________
23 x
__________
32 x1
_________
c. The following table represents an exponential function. Fill in the blanks AND write the
equation of the exponential function.
x
y
0
1
2
3
3
d. Express the following expression as a power of 10.
4
1
 10
10000000
__________________
4
5
6
16/27
7
3. Exponential Growth and Decay
a. For each of the following, determine the rate of growth or decay. Write your answer in the blank
provided. Be sure to indicate whether your rate is growth or decay. You can write your answer
as a decimal, a percent, or in exact form.

y  100  (0.85) x
__________

A bacterial population triples every day.
__________

An isotope with a half-life of 200 hours.
__________

y  250  (3) x /2
__________

The population described by this table
__________
x
P(x)
1
10
3
15
7
33.75
b. Circle the data set below which represents an exponential function and write an exponential
model of the form y  ab x right below it.
Option 1
x
1
3
4
8
Option 2
y
75.00
42.19
31.64
10.01
x
1
3
4
8
y
107.50
82.50
70.00
20.00