Properties of Logarithms
Logarithmic & Exponential Form
Logarithmic Equations
Exponential Growth & Decay
"e"
Exponential Equations
Word Problems
100
If there is no base in a logarithm what does it automatically equal?
10
100
Evaluate
3
100
what is the first step when solving this logarithmic equation called?
2log(x-5)+3log(x+3)=5
Condensing the logarithm
100
Whats the formula for exponential growth?
f(t)=a(1+r)t
100
logarithmic functions with base "e" are called what?
natural logarithm
100
Solve for x:
316(2^x)=79
x=-2
100
what is the (a-value) 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 answer.
$150
200
In a logarithm subtraction goes with what?
Division
200
Evaluate 
DNE
200
If
log_a(x)=log_a(7), then
x=7
200
Whats the formula for exponential decay?
f(t)=a(1-r)t
200
what is the value of "e"
2.71828......
200
Solve for x, round to the nearest 100th.
14e^(x/4)=168
x=9.94
200
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'll have in t years
f(t)= 813(1+.013)^(12t)
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 base and a negative argument
300
How many decimal points must you move over in order to have the correct rate?
How would you rewrite this percentage?
3%
two decimal points.
.03
300
Write this equation in logarithmic form:
e^x=24
ln24=x
300
Solve for x to the nearest 100th.
2^(5x)=94
x~~1.31
300
$13,695.98
400
Where should you move the exponent to?
logkmw
the front: wlogkm
400
convert into logarithmic form:132=169
log13169=2
400
Solve: log9(6-3w)=log9(-2w)
No Solution
400
Solve for x. Round your answer to the nearest ten thousandths.
x= - 6.1421
400
condense this expression into a single logarithm:
2ln3+ ln6
ln(54)
400
Solve for x to the nearest whole number
27=480(.945)^(.17x-3)-29
x~~241
400
$21,360.01
500
Condense: 2log38=
log382=log364
500
convert into log form:
8^x= 6
log86=x
500
Solve: log468-log44=log4(3n+11)
n=2
500
A new car is purchased for $44,000 and over time its value depreciates by one half every 6 years. Write a function showing the value of the car after t years, where the annual decay rate can be found from a constant in the function. Determine the percentage rate of decay per year, to the nearest hundredth of a percent.
f(t)=44000(.89)^(t)
r~~10.91 %
500
expand this logarithm:
ln (3x)
ln 3+ln x
500
Solve for all values of x
8^(4x+26)=2^(2x^2-2)
-4, 10
500
Sarah is going to invest $79,000 and leave it in an account for 7 years. Assuming the interest is compounded quarterly, what interest rate, to the nearest tenth of a percent, would be required in order for Sarah to end up with $121,000?
r=6.1 %
600
Evaluate.
64
600
Condense the following logarithm:
log_4((x^3z^2)/y^5)
600
log_(x+5)(2x^2-14)=2
13, -3
600
In a lab experiment, 150 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every 24 hours. Write a function showing the number of bacteria after t hours, where the hourly growth rate can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage of growth per hour, to the nearest hundredth of a percent.
f(t)=150(1.0293)^(t)
r~~2.93%
600
What is the base of the logarithmic expression?
10
600
True or False? Explain your answer.
True
600
Jack is going to invest $650 and leave it in an account for 6 years. Assuming the interest is compounded continuously, what interest rate, to the nearest hundredth of a percent, would be required in order for Jack to end up with $840?
A=Pe^(rt)
r=4.27%