7.1 Growth/Decay Models
7.2 Inverse Functions
7.3 Meaning of Logarithms
7.4 Properties of Logarithms
7.5 Logarithmic/exponential Equations
100
Is this equation exponential?
h(x)=3x^7-2
NO, the x has to be in the exponent to be considered exponential, the exponent in this case is simply a number.
100
Find the inverse:
h(x)=(2x+3)/5
h^-1(x)=(5x-3)/2
100
Simplify
log_(123453145)1
0
100
Evaluate
log_3(81*243)
9
100
Solve:
x=sqrt2
200
Some real estate agents estimate that the value of a house could increase about 4% each year. Write a function to model the growth in value for a house initially valued at $100,000
f(x)=100,000(1.04)^x
200
Find the inverse of
f(x)=6^x
f^-1(x)=log_(6)x
200
Simplify
log_(2)64
6
200
Simplify
log125+log80
4
200
x=?
x=68
300
Some real estate agents estimate that the value of a house could increase about 4% each year. A house is valued at $100,000 in 2005. Predict the year its value will be at least $130,000
2012
300
Find the inverse of
g(x)=sqrt(x^3+1
g^-1(x)=(x^2-1)^(1/3)
300
Simplify the expression
log_(64)4
1/3
300
Combine under one log
20log_(6)u-5log_(6)v
log_(6)(u^6/(v^5))
300
What value of x satisfies this equation?
x=0.903
400
A certain car depreciates about 15% each year. Suppose the car was worth $20,000 in 2010. What is the first year that the value of this car will be worth less than half of that value?
2015
400
What is the inverse?
y=6^(x/4)
y=log_(6)x^4
400
Evaluate the expression
log_(2/3)(81/16)
-4
400
Simplify
log_(6)(1/6^4)^3
-12
400
Solve for the unknown variable.
x=+- 20
500
During the winter months, insects die off at a rate of 2% per week. Assuming the population of insects at a park in Piscataway is 4834, how many insects are left after 16 days?
4616 Insects
500
What is the inverse of the equation below?
y=(5^x-7)^(1/4)
y=log_(5)(x^4+7)
500
?
log_(32)128
7/5
500
Show proof:
C
500
This is going to take some voodoo
x=(3/10)^(1/3)