Logarithms
Write the following logarithmic equation as an exponential equation:
log_(3)81=4
3^4=81
In 2010, a half pound beef n' cheddar cost $6.99. However, each year, the price increased by 2%. What is the growth factor of the half pound beef n' cheddar?
1.02
Write an exponential equation that has a growth factor of 3 and has a value of 20 when x = 0
y=20(3)^x
Solve the following equation for x:
64=4^x
3
Write the following exponential equation as a logarithmic equation:
4^x=64
log_(4)64=x
The cost of a McChicken x years since 2010 can be modeled by the function below. In it, what does 3 represent?
f(x)=3(1.03)^x
In 2010, a McChicken cost $3
Write an exponential function that has a growth factor of 0.67 and an initial value of 1738
y=1738(0.67)^x
Solve the following equation for b:
log_b(400)=2
20
Write the following exponential equation as a logarithmic equation:
m^n=p
log_(m)p=n
The cost of a McChicken x years since 2010 can be modeled by the function below. In it, what does 1.03 represent?
f(x)=3(1.03)^x
Each year the cost of a McChicken increases by 3% or by a factor of 1.03
The population of Vilonia Arkansas was 3,500 in 2015 and has grown by 1.5% each year since then. Write a function that represents the population of Vilonia
y=3500(1.015)^x
Solve the following equation for a:
150=a(1.75)^10
0.56
Write the following logarithmic equation as an exponential equation:
log_(b)(1000/30)=15
b^15=(1000/30)
The cost of a McChicken x years since 2010 can be modeled by the function below. What would f(-10) mean in this scenario?
f(x)=3(1.03)^x
The cost of a McChicken in 2000
The number of members at a gym is growing exponentially. Write a function that represents the number of members each month if there were 160 members initially, then 200 members the next month.
y=160(1.25)^x
Solve the following equation for a:
-15=a(2.3)^5
-0.233
Write the following exponential equation as logarithmic equation. Simplify:
2(3)^x=100
log_(3)(50)=x
The cost of a McChicken x years since 2010 can be modeled by the function below. What was the original cost of a McChicken when it was released in 1980?
f(x)=3(1.03)^x
$1.24
Initially, a species of bacteria covers 0.1% of a pond. Every day, the area it covers doubles. Write an equation that represents this. How much will be covered after 8 days?
y=0.1(2)^x
25.6% of the pond
The value of a baseball card t years after it was purchased is represented by the function below. How many years will it take for the card to be worth $100?
f(t)=40(1.03)^t