Properties of Exponents
Simplify
((5u^7)/(2v^3))^4
(625u^28)/(16v^12
What is the domain and range of the following function
f(x)=-5/2 (3)^(x+2)-1
\text(Domain: ) (-\infty,\infty)
\text(Range: ) (-\infty,-1)
Express as a sum/difference of logarithms
log_a \sqrt{\frac{a^6b^8}{a^2b^5}
2+\frac{3}{2}log_a b
Solve the following equation
\ln(5x-4)=3
4.8171
Find the exponential function that contains the points
(2,48) and (3,192)
f(x)=3\cdot 4^x
Simplify
((t^2)^5(t^4)^2)/(t^3)^7
1/t^3
What is the Domain and Range for the following Function?
f(x)=2(3)^(x+2)
\text(Domain: ) (-\infty,\infty)
\text(Range: ) (0,\infty)
Express as a sum/difference of logarithms
log \sqrt{r^3t}
\frac{3}{2}log r + \frac{1}{2}log t
Solve the following equation
\log (-4x+42)=1
8
Find the exponential function that passes through the points (1,-20) \text{ and } (2,-80)
f(x)=-5\cdot 4^x
Simplify
(y^23)/(y^17)
y^6
What is the domain and range for the following function?
f(x)=-\frac{7}{2}(5)^(x-2)+1
\text(Domain: ) (-\infty,\infty)
\text(Range: ) (-\infty,1)
Simplify to a single logarithm
log(x^2-4)-log(x+2)
log(x-2)
Solve the following equation
log_2(-6x+46)=4
5
9 Hours
Simplify
(-93c^7d^15)^0
1
What is the Domain and Range for the Following Function?
f(x)=\sqrt(x+1)
\text(Domain: ) [-1,\infty)
\text(Range: ) (-\infty,\infty)
Simplify to a single logarithm
log_a \frac{a}{\sqrt{x}}-log_a \sqrt{ax}
\frac{1}{2}-log_a x
Mai invests $20,000 at age 20. She hopes the investment will be worth $500,000 when she turns 40. If the interest compounds continuously, approximately what rate of growth will she need to achieve her goal?
A=Pe^(rt)
16.1%
The number of users on UL's website has grown exponentially since it was redone. After 2 months, there were 200 viewers. After 4 months, there were 800 viewers. Construct a model to explain this growth.
f(x)=50\cdot 2^x
Find the Quotient
(64x^10y)/(-14x^12y^4)
-(32)/(7x^2y^3)
What is the domain and range for the following function?
f(x)=\frac{3}{\sqrt{x+4}}
\text(Domain: ) (-4,\infty)
\text(Range: ) (0,\infty)
Simplify
log_p p^3
3
Natasha invests $3,000 at age 18 from the signing bonus of her new job. She hopes her bonus will yield $300,000 when she hits 40. What's the growth rate she'll need if she wants to hit her goal?
A=Pe^(rt)
20.9%
The selling price of a car is $18,000. Each year, it loses 15% of its value. Build a function to explain the loss in value of this car.
f(t)=18,000(0.85)^t
Simplify
((-2p^2)^4(3p^4)^2)/(-6p^3)^2
4p^10
Find the inverse of the following function
f(x)=\frac{-6x+8}{-8x+2}
f^(-1)(x) = \frac{4-x}{3-4x}
Simplify
ln e^(8t)
8t
Solve the following equation
2\ln x - \ln 5 = \ln (x+10)
10
Write an exponential function for the following scenario.
The value, V, of an investment of $1000 which grows continuously at a rate of 1.4% per year.
V(t)=1000e^{0.014t}
Simplify
((-4m^3)^2(5m^4)^3)/(-10m^6)^3
-2
Find the inverse for the following function
f(x)=-2x^2+6
f^-1(x)=\sqrt{-\frac{x+6}{2}}
Simplify to a single Logarithm
\frac{3}{2}\ln4x^6-\frac{4}{5}\ln 2y^(10)
ln \frac{2^{\frac{11}{5}}x^9}{y^8}
Solve the following equation
log_4(x+3)+\log_4(x-3)=2
5
The population of a certain town, in thousands of people, is given by
P(t)=60(1.034)^t
where t is given in years since 2005.
a) What is the population in 2005?
b) What is the growth rate as a percentage?
c) What was the population in 2008?
d) When will the population be 100,000 people?
a) 60,000 people
b) 3.4%
c) About 66,330 people
d) 2020