WorksheetsExponential and Log review
Total questions: 150
Worksheet time: 9hrs 29mins
Rewrite logx95 = 2.3
x2.3 = 95
952.3 = x
2.395 = x
x95 = 2.3
Without a calculator, determine which of the following yields a negative answer.
log9 (1/30)
log9 3
log9 -81
log9 1
Without a calculator, evaluate log41
1/4
0
-1
not possible
Without a calculator, list the following in order, least to greatest:
A) log5 30
B) log0.25 32
C) log7 49
D) log8 40
A,B,C,D
A,B,D,C
B,D,C,A
B,D,A,C
Without a calculator, determine which of the following ISN"T possible. Check all that apply.
log2 (x - 4) when x = 4
log3 (x+3) when x = 0
-2log5 (x-1) when x = 0
1/2 log (x+4) when x = -2
Without technology, determine which of the following is an increasing function. Check all that apply.
y = log2 (x - 4)
y = log3 (x+3)
y = -2log5 (x-1)
y = 1/2 log x + 4
Which of the following has a domain of all real numbers, x > 2 ?
y = log2 x
y = log3 (x+2)
y = log4 (x - 2)
y = log7 x - 2
Without a calculator, evaluate log125 25
2/3
3/2
1/6
1/5
Which of the following is the sketch of the graph of y = -log3 (x+5) ?
Without a calculator, evaluate log6 -36
not possible
-2
2
1/2
log(4x)
log4-logx
log4+logx
4logx
xlog4
log(xy2)
logx+2logy
logx+logy2
logx-2logy
logx+logy+log2
log(yx)
logx+logy
xlogy
log(x-y)
logx-logy
log(nm3)
logm-log3-logn
3logm+logn
3logm-logn
3log(m-n)
log(3x)2
2log(3+x)
2log3+logx
log3+2logx
2(log3+logx)
ln(z42x2y)
ln2+2lnx+lny+4lnz
ln2+2lnx+lny-4lnz
2ln(2xy)-4lnz
2ln2x+lny-4lnz
log2x - 5log2y
Which of the following does NOT describe the graph of the logarithmic parent function?
The graph has a domain of all positive real numbers.
The graph has a range of all real numbers.
The x-intercept is 1.
The x-axis is the horizontal asymptote.
f(x)=log5(x+4) - 2
Describe the asymptote
Horizontal Asymptote x = -4
Vertical Asymptote x = -4
Horizontal Asymptote x = 4
Vertical Asymptote x = 4
f(x)=log5(x+4) - 2
Find the Domain and Range
Domain: x ≥ -4
Range: all real numbers
Domain: all real numbers
Range: y ≥ -4
Domain: all real numbers
Range: y > -4
Domain: x > -4
Range: all real numbers
f(x)=log5(x+4) - 2
Describe the transformation
translation 4 units to the right, 2 units down
translation 4 units to the left, 2 units down
translation 4 units to the up, 2 units right
translation 4 units to the up, 2 units left
f(x)=2ln(x+2)
Describe the asymptote
Horizontal asymptote x = -2
Horizontal asymptote x = 2
Vertical asymptote x = -2
Vertical asymptote x = 2
f(x)=2ln(x+2)
Find the Domain and Range
Domain: (-∞, ∞)
Range: ( -2, ∞)
Domain: (-∞, ∞)
Range: ( -∞, -2)
Domain: ( -∞, -2)
Range: (-∞, ∞)
Domain: ( -2, ∞)
Range: (-∞, ∞)
f(x)=2ln(x+2)
Describe the transformation
Vertical Stretch by 2, translation 2 units to the left
Vertical Compression by 2, translation 2 units to the left
Vertical Stretch by 2, translation 2 units to the right
Vertical Compression by 2, translation 2 units to the right
f(x)=¼ ln(x - 2) + 3
Describe the asymptote
Horizontal asymptote x=2
Horizontal asymptote x= -2
Vertical asymptote x=2
Vertical asymptote x= -2
f(x)=¼ ln(x - 2) + 3
Find the Domain and Range
Domain: all real numbers
Range: y > 2
Domain: all real numbers
Range: y > -2
Domain: x > -2
Range: all real numbers
Domain: x > 2
Range: all real numbers
f(x)=¼ ln(x - 2) + 3
Describe the transformation
Vertical Stretch by 1/4, translation 2 units right, 3 units up
Vertical Compression by 1/4, translation 2 units right, 3 units up
Vertical Stretch by 1/4, translation 2 units left, 3 units up
Vertical Compression by 1/4, translation 2 units left, 3 units up
How many employees will there be after 3 years?
Describe the tranformation
translate 4 units up
translate 4 units left
translate 4 units right
translate 4 units down
A=1200(.85)6
What is the initial value of the situation represented by f(x)=0.05(2)x?
0.05
2
0.1
1
Domain of y = log x ?
All real numbers
x>0
x<0
y>0
Write the equation for the graph.
f(x) = log2 (x-3)
f(x)= 3 log2(x)
f(x) = log2(x+3)
f(x) = log2(x) + 3
LNe
What is the Domain?
What is the Range?
Is the function INCREASING or DECREASING?
Is the function INCREASING or DECREASING?
What is the Initial Amount?
How many employees will there be after 3 years?
Determine the horizontal asymptote for the function
f(x) = 3(2)x-4 + 5
x=4
y=4
x=5
y=5
A=1200(.85)6
Domain of y = log x ?
All real numbers
x>0
x<0
y>0
Florine-21 has a half-life of 4 seconds. You begin with a 50 mg sample of Florine-21.
Which exponential equation would represent the amount of Florine-21after t seconds.
f(t)=50(21)2t
f(t)=50(21)t2
f(t)=50(21)t4
f(t)=50(21)4t
Prescription A has an initial value of 1200 mg/L and a half-life 6 hours. Which equation will help us determine the remaining level after 1 day?
y=1200(21)61
y=1200(21)624
y=1200(21)16
y=1200(21)246
Identify the common ratio (b value) of the function f(x)=2(4)x.
2
4
(2)x
8
In an exponential function, what does the 'a' represent?
Slope
Rate of change
Y-intercept
Multiplier
Is the population of elephants increasing or decreasing?
Identify the function y = 100(6x) as an example of exponential growth or decay. What is the y-intercept?
exponential decay; y-intercept: 6
exponential decay; y-intercept: 100
exponential growth; y-intercept: 6
exponential growth; y-intercept: 100
The population of wolves in a certain place was 5,450 in 2013. Each year the population has decreased by 5%. What equation models the population of wolves since 2013?
p(x) = 5450 - 95x
p(x) = 5450(0.05)x
p(x) = 5450(0.95)x
p(x) = 5450 (1.05)x
A savings account earns interest at an annual rate of 2.89%, compounded quarterly. If the account begins with a principal amount of $6000, what will be its total value after 5 years?
$6,328.25
$6,929.17
$6,809.18
$6,500.78
What exponential equation can we create to model this situation?
I think this graph represents a growth. How accurate am I in my assertion?
You are correct. b value is greater than 1
You are incorrect. b value is less than 1
Which does the graph represent?
Growth
Decay
What is the percent (%) of increase or decrease in the following function?
f(x) = 3000 (1 + 0.4)x
Decrease by 4%
Increase by 4%
Increase by 40%
Decrease by 40%
What is the percent (%) of increaase or decrease in the following equation?
f(x) = 250 (0.95)x
Decrease by 95%
Increase by 5%
Decrease by 5%
Increase by 95%
The same amount of principal is invested in different accounts earning the same interest rate. Which of the following accounts would have the greatest accumulated value at the end of one year?
An account earning no interest
An account earning interest compounded monthly
An account earning interest compounded annually
An account earning interest compounded daily
What does the n stand for in this formula?
Initial amount
Final amount
Rate
Time
The number of times compounded per year
What does the P stand for in this formula?
Initial amount
Final amount
Rate
Time
The number of times compounded per year
You deposit your life savings into Batrez Bank in the hopes it will double in 15 years. If Batrez Bank compounds quarterly, what interest rate are you hoping for?
4.64%
4.65%
13.9%
4.63%
At 4% annual interest compounded quarterly, how long will it take to double your money?
0.4 yrs
16.4 yrs
17.4 yrs
18.4 yrs
You invest $1600 at an annual interest rate of 4.6% compounded continuously. How much will you have in the account after 4 years.
$1,923.23
$10,138.07
$6,701.28
$800.26
log4(3x-1)=log4(2x+3)
4
3
1
8
logx1000=3
1
10
30
3
log8(4x+4)=2
15
12
10
3
log x + log 8 = 2
log x - log 8 = 3
Solve for x
1.792
403.4
16.31
-1.792
Solve for x
22026
27.18
4.605
2.303
Solve for x
1.099
0.549
0.405
2.197
Solve for x
1.609
0.792
1.792
1096
Solve for x
0.564
0
0.693
1.079
Solve for x
1.354
1808
4.029
2.015
Solve for x
20.086
1.099
8.155
-1.099
Solve for x
-0.916
1.087
1.492
0.083
Solve for x
1.221
0.746
1.492
2.226
Solve for x
12.182
-0.351
3.649
1.307
Solve for x
2.226
6.677
0.742
1.075
Rewrite ex = 9 using a logarithm
ln x = 9
ln 9 = x
logx e = 9
log9 x = e
3e2x + 10 = 25
{-3.940}
{1.228}
{0.451}
{0.805}
ln(2) = x
7e(3x-5) = 49
A certain college has been raising tuition every year since the year it opened. The function T = 12,000 (1.03)x represents the tuition, T, after x years.
If the college opened in the year 1990, what would you predict the tuition will be in the year 2020?
$29,127
$2,020
30 years
Write an equation that models the following situation:
The current student count at John Jay is 6500, it is expected to grow at a rate of 14% next year.
y= 6500(1+.14)x
y= 6500(1-.14)x
y= 6500(14)x
y= 14(6500)x
What is the Growth/Decay factor of the function f(x)= 2(4)x ?
2
8
4
x
What is the asymptote of y = 2x - 3
y = 0
y = -3
x = 0
x = -3
What is the asymptote of y = log2x - 3
y = 0
y = -3
x = 0
x = -3
What is the asymptote of y = log2(x - 3) ?
y = 0
y = 3
x = 0
x = 3
What is the asymptote of y = log2(x - 3) ?
y = 0
y = 3
x = 0
x = 3
