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WorksheetsExponential and Logarithm Functions
Total questions: 25
Worksheet time: 2hrs 12mins
Name
Class
Date
1.
Change to Exponential Form:
log636 = 2
log636 = 2
a)
26=36
b)
62=36
c)
362=6
d)
366=2
2.
Change to Logarithmic Form:
53 = 125
53 = 125
a)
log 5 125 = 3
b)
log 3 125 = 5
c)
log 5 3 =125
d)
log125 3 = 5
3.
Condense to a single logarithm.
a)
ln x4/ y
b)
ln xy4
c)
ln x/ y4
d)
ln x4/ y4
4.
Condense.
a)
log2x2y10
b)
log2x2+log2y10
c)
log2x2/y10
d)
log210xy
5.
Expand.
a)
log x + 5 log y
b)
5 log x + 5 log y
c)
5 log x - log y
d)
log x - 5 log y
6.
Condense
a)
logxyz3
b)
log(xy/z3)
c)
logx+logy+logz3
d)
logx3y3z3
7.
Expand
a)
6log8v-2log8u
b)
6log8u-2log8v
c)
3log8u-2log8v
d)
6log8u+2log8v
8.
Riley invested $1,000 in savings bonds. If the bonds earn 6.75% interest compounded semi-annually, how much total will Riley earn in 15 years?
a)
$1,584.62
b)
$2,651.39
c)
$2,706.86
d)
$1,825.10
9.
Olivia would like to buy some new furniture for her home. She decides to buy the furniture on credit with 9.5% interest compounded quarterly. If she spent $7,400, how much total will she have paid after 8 years.
a)
$15,415.94
b)
$15,683.28
c)
$15,927.56
d)
$16,109.05
10.
Approximately what interest rate would be needed in order to grow an investment of $1,400 to $2,500 in 10 years if the interest was compound monthly?
a)
5.96%
b)
5.84%
c)
5.81%
d)
5.88%
11.
If $1,000 is invested at 16% interest, compounded continuously, for five years, what is the ending balance?
a)
$1,225,54
b)
$2,225.54
c)
$22,255.40
d)
$225.54
12.
Use the change of base formula and your calculator to approximate the log.
a)
A
b)
B
c)
C
d)
D
13.
Use the change of base formula and your calculator to approximate the log.
a)
A
b)
B
c)
C
d)
D
14.
Rewrite in exponential form.
a)
A
b)
B
c)
C
d)
D
15.
Solve the equation.
a)
A
b)
B
c)
C
d)
D
16.
log2(x + 5) = 3
a)
3
b)
4
c)
5
d)
6
17.
Solve:
log (4x − 5) = log (2x − 1)
log (4x − 5) = log (2x − 1)
a)
0
b)
1
c)
2
d)
3
18.
The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the exponential equation?
a)
y=8(15,000)x
b)
y=15,000(1.08)x
c)
y=15,000(0.92)x
d)
y=15,000(0.08)x
19.
What would the change base look like for:
log6 48
log6 48
a)
log 8
b)
log 6/log 48
c)
log 48/log 6
d)
ln 8
20.
In an exponential function, what does the 'a' represent?
a)
SLOPE
b)
RATE OF CHANGE
c)
STARTING VALUE
(y-intercept)
(y-intercept)
d)
GROWTH FACTOR
21.
In an exponential function, what does the 'b' represent?
a)
SLOPE
b)
GROWTH FACTOR
c)
Y-INTERCEPT
d)
STARTING VALUE
22.
The inverse of a logarithmic function and the logarithmic function do what on a graph?
a)
The are perpendicular
b)
They are paralell
c)
They reflect over the line y=x.
d)
There is nothing special .
23.
Write log2 0.25 = -2 in exponential form
a)
-22 = 0.25
b)
-20.25 = 2
c)
2-2 = 0.25
d)
No correct answer
24.
Which of the following represent the a change of base for logx y using the natural log?
a)
ln x / ln y
b)
ln y / ln x
c)
log x / log y
d)
log y / log x
25.
Expand.
a)
1/3 log x + log y + log z
b)
1/3 log x + 1/3 log y + 1/3 log z
c)
1/3 log x - 1/3 log y - 1/3 log z
d)
3 log x + 3 log y + 3 log z
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