7.1 Growth/Decay Models
7.2 Inverse Functions
7.3 Meaning of Logarithms
7.4 Properties of Logarithms
7.5 Logarithmic/exponential Equations
More 7.3
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
log(5x-1)=log(x+7)
x=2
100
Rewrite in logarithmic form
3^7=2187
log_(3)2187=7
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)32
5
200
Simplify:
log_(8)80-log_(8)10
1
200
x=?
x=68
200
Evaluate using mental math
log100,000
6
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_(2)(1/16)
-4
300
Simplify
log125+log80
4
300
Solve:
x=sqrt2
300
Evaluate using mental math
log_(4)256
4
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
log_(16)4
1/2
400
Evaluate
5log_(4)4-4log_(2)2
1
400
What value of x satisfies this equation?
x=0.903
400
Simplify:
10^(logx)+log_(5)5^x
2x
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
Simplify
log_(6)(1/6^4)^3
-12
500
Solve for the unknown variable.
x=+- 20
600
Show proof:
C
600
This is going to take some voodoo
x=(3/10)^(1/3)