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)`