Properties of Logs
Solving Logs
Transforma-tions
Graphing (no calc)
Interest Formulas
Arithmetic & Geometric
Evaluating Logs (no calc)
100
Fully expand the below logarithm.
log8(a3b)
3log8a+log8b
100
Solve the below equation for x.
log11(2x-3)=log11(3-x)
x=2
100
Use f(x) to describe the transformation that results in the graph of g(x).
f(x)=logx
g(x)=½log(x)+2
-Vertical compression by a factor of ½.
-Translation 2 units up
100
Graph the following function.
f(x)=log2(x)+1
100
In 2022, Ananya bought a car for $15,000 and its value is expected to depreciate by 13% each year. How much will the car be worth in 2030
$4923.18
100
Arithmetic, Geometric, or Neither:
4, -10, -24, -38
arithmetic
100
Evaluate the below logarithm.
log327
log327 = 3
200
Fully condense the below expression to a single logarithm.
13log2x-5log2y
log2[(x13)/(y5)]
200
Solve the below equation for all possible values of x.
ln(m2-3)=ln(m+3)
x=+3
x=-2
200
Based on the transformation described below, write a new function, g(x), from the parent function f(x).
f(x)=lnx
g(x)=f(x) translated 4 units up, reflected over the y-axis, vertical stretch by a factor of 5
g(x)=5ln(-x)+4
200
What is the end behavior of this function:
End Behavior:
lim_(x->oo) f(x)=oo
lim_(x->-3^+) f(x)= -oo
200
Erin deposits $300 into an account that has a 5% interest rate, compounded monthly. After 8 years, how much money will Erin have in her account? Round to the nearest hundredth.
$447.18
200
Determine a20 for this arithmetic sequence:
4, 7, 10
61
200
Evaluate the below logarithm.
5log512
5log512 = 12
300
Fully condense the below expression to a single logarithm.
2log23+5log2x-3log2y
log2[(9x5)/(y3)]
300
Solve the below equation for x.
log3(4x+5)-log311=1
x=7
300
Use the parent function to describe the transformation that results in the graph of g(x).
g(x)=-log(1/3x)- 8
-Reflection over the x-axis.
-Horizontal stretch by a factor of 3.
-Translation down 8 units
300
State the asymptote of the following function
f(x)=(2)x-3-4
y = -4
300
Bartholomew has $500 and wants to deposit it into an interest-bearing account that compounds continuously in order to have $1,050 in 6 years. What interest rate would he need to meet this goal? Report your answer as a whole number percentage.
12%
300
If the common ratio is 2 and a5=-96, find a1
a1 = -6
300
Evaluate the below logarithm.
log root(3)10
1/3
400
Fully expand the below logarithm.
log[(b4)/(25x)]
4logb-2log5-logx
400
Solve the below equation for x. Round to the nearest hundredth.
4-x=17
x = -2.04
400
Use f(x) to describe the transformation that results in the graph of g(x).
f(x)=log11x
g(x)=log11(4x+36)
-Horizontal compression by a factor of ¼.
-Translation 9 units to the left
400
Is this function increasing or decreasing? How do you know?
f(x) = 4(0.5)x+1+6
decreasing
b value is between 0 and 1
400
In 2015, Village Town had a population of 3.68 million people. If the population continuously grows at a rate of 3%, in what year will the population exceed 5 million?
2025
400
In an arithmetic sequence where a1=4 and a7=-32, find a25
a25=-140
400
Evaluate the below logarithm.
log162
log162 = 1/4