Properties of Logarithms
Logarithmic & Exponential Form
Logarithmic Equations
Exponential Growth & Decay
"e"
100
If there is no base in a logarithm what does it automatically equal?
10
100
what is the equation for logarithmic form?
logba=x
100
Solve the equation.
2logx=4
10000
100
Whats the formula for continuous compound interest?
PERT
100
logarithmic functions with base "e" are called what?
natural logarithm
200
logA-logB=?
log(A/B)
200
what is the formula for exponential form?
bx=a
200
Solve the equation.
ln(4x+3)=ln(2x+7)
2
200
Whats the formula for compound interest?
A=P(1+r/n)nt
200
what is the value of "e"
2.71828......
300
LogA+LogB=?
Log(AB)
300
convert into exponential form: log39=2
32=9
300
At the end when checking your answer what can NOT be in the logarithmic equation?
A negative
300
How would you rewrite this percentage in decimal form?
3%
two decimal points.
.03
300
Write this equation in logarithmic form:
ln24=x
400
Where should you move the exponent too?
logkmw
the front: wlogkm
400
convert into logarithmic form:132=168
log13168=2
400
Solve: log9(6-3w)=log9(-2)+log9(w)
No Solution
400
what is the principal in the following word problem?
Lilly bought a new bike for $150 in 2020. If the bikes value goes down by 15% each year write an exponential function to model the situation.
Note: you do not have to write an equation just find the (a).
$150
400
condense this expression into a single logarithm:
ln 3+ ln 6
ln(48)
500
Condense by moving the exponent: 2log38=
log382=log364
500
convert into log form: 83= 6
log86=3
500
Solve: log468-log44=log4(3n+11)
n=2
500
Write an exponential growth equation from the following word problem and solve.
In 2021, Kenny gained 813 followers on TikTok over a month. If his followers increase by 1.3% each month write an exponential function to find the number of followers he will have in a year.
f(12)= 813(1+.013)12
500
expand this logarithm:
ln (3x)
ln 3+ln x
600
Evaluate. Use a calculator if need be.
64
600
Evaluate 
DNE
600
37 years
600
$21,360.01
600
What is the base of the logarithmic expression?
10
700
Evaluate.
3
700
log_4((x^3z^2)/y^5)
700
Solve for x. Round your answer to the nearest ten thousandths.
x= - 6.1421
700
$13,695.98
700
True or False?
True