Conceptual Understanding
Exponential vs Logarithmic Form
Key Characteristics of Graphs of Exponential and Logarithmic Functions
Evaluating Logarithms
Properties of Logarithms
Solving Logarithmic Equations
Solving Exponential Equations
Applications
100
A logarithm is another way of writing
What is an exponent?
100
Rewrite in exponential form:
log_3(81)=4
What is 3^4=81 ?
100
The exponential behavior shown by the graph
What is exponential growth?
100
The value of log_5(625)
What is 4?
100
Expand log(ab)
What is log(a)+log(b)?
100
Solve:
log_5(x)=log_5(6)
What is x=6?
100
Solve:
2^x=32
What is x=5 ?
100
The formula A=P(1+r/n)^(nt) represents
What is compound interest?
200
The base in an exponential function
What is the constant number being raised to a power?
200
Rewrite in logarithmic form: 4^(7/2)=128
What is log_4(128)=7/2?
200
This is the horizontal asymptote of the function shown.
What is y=4 ?
200
The value of log_9(1/81)
What is -2?
200
Condense log(x)-log(y)
What is log(x)/log(y) ?
200
Solve:
log_7(x)=3
What is x=343 ?
200
Solve:
(1/2)^x=8
What is x=-3 ?
200
The formula y=Pe^(rt) represents
What is continuous growth?
300
The key difference between exponential growth and exponential decay
What is growth has base b>1 and decay has 0<=b<1 ?
300
Rewrite in exponential form:
log_(1/2)(32)=-5
What is (1/2)^-5=32?
300
This is the vertical asympote of the function shown.
What is x=-3 ?
300
The value of log_16(2)
What is 1/4 ?
300
Expand: log_5(x^4/y^2)
What is 4log_5x-2log_5y?
300
Solve:
ln (x-1)=2
What is x=e^2+1 ?
300
Solve:
3^x=10
What is x=log_3(10)?
300
Kevin started his new job with a salary of $26,550. Every year, he receives a 3.15% increase in his salary. Write an exponential growth model to find his salary after 20 years.
What is
y=26550(1+0.0315)^20
$49,368.41 ?
400
True or False: Exponetial and logarithmic functions of each other.
What is true?
400
Rewrite in exponential form:
ln8=2.08
What is e^2.08=8 ?
400
This interval describes where the function is decreasing.
What is (- infty,infty) ?
400
The value of log_4(sqrt(4))
What is 1/2 ?
400
Condense: 1/2(ln64+5 lnk)-4lnm
What is ln ((8sqrt (k^5))/m^4) ?
400
Solve:
log_8(7-5w)+2=11/2
What is w=-5 ?
400
Solve:
5^(2x-1)=12
What is (log_5(12)+1)/2 ?
400
An investment account starts with $2000 at a 4% interest rate compounded continuously. If no other withdrawals are made, find the balance of the account after 50 years.
What is y=2000e^(0.04(50))
$14,778.11 ?
500
The expression log_ba=x in exponential form is
What is b^x=a ?
500
Rewrite in logarithmic form:
e^4=54.6
What is ln 54.6=4 ?
500
This is the domain of the function shown.
What is (2,infty)?
500
Using common logarithms, express the value of log_7(20)
What is (log20)/log7 ?
500
Condense:
2log_3(x-4)+log_3(3x)
What is log_3(3x^3-24x^2+48x)?
500
Solve:
log(3x^+4x)=log(2x^2+12)
What is x=-6 and x=2 ?
500
Solve:
-6e^(x-2)-5=144
What is ln(139/6)+2 ?
500
Jonathan deposits $1500 into a savings account earning 3.79% annual interest compouned daily.If he makes no other deposits or withdrawals, find his account balance after 15 years.
What is y=1500(1+0.0379/365)^(365(15))
=$2,648.35 ?