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
What is the first step when solving logarithmic equations with multiple logs?
Condensing the logarithm
100
What's the formula for exponential growth?
A(t)=p(1+r)t
100
logarithmic functions with base "e" are called what?
natural logarithm
200
In a logarithm subtraction goes with what?
Division
200
What is the formula for exponential form?
bx=a
200
If two logs have the same base then what can you do?
Cross them out and solve like a regular math equations.
200
What's the formula for exponential decay?
A(t)=p(1-r)t
200
what is the approximate value of "e"
2.71828......
300
In a logarithm adding goes with what?
Multiplication
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 many decimal points must you move over in order to have the correct (b)?
How would you rewrite this percentage?
3%
two decimal points.
.03
300
Write this equation in logarithmic form:
ex=24
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(-2w)
No Solution
400
What is the (p) 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 (p).
$150
400
condense this expression into a single logarithm:
ln 3+ ln 6
ln(48)
500
Condense: 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.
64
600
Evaluate 
DNE or no solution
600
2+2 =
4
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