Logs Review

Log Properties

100

3ln2 + 5ln2 - ln3

ln (256/3)

200

What is the 91st term in the sequence?

11, 4, -3, -10...

-619

300

1/2log(9) + log(2xy)

log(6xy)

400

2log₅(5x) + log₅y - log₅(x+1)

log₅(25x²y/x+1)

500

5(log2x - logy) - (log3 + 2log5)

log(32x⁵/75y⁵)

Exponential Functions

100

The function f(x)=10000(0.8)^x models the value of a house, where x is measured in years. 

A. Does this represent exponential growth or decay?

B. By what percent does the house's value increase/decrease every year?

A. decay

B. 20%

200

What is the equation of the asymptote for the function y=3^x-3

y=0

300

Make a table of values with at least three points that you would use to graph the function y=3^x-1+2. 

Hint: start with parent function y=3^x, then apply shifts.

Any three of the following: (0,7/3), (1,3), (2,5), (3,11), (4,29)

400

Write an exponential function with the points (1, 12) and (5, 972).

y=4(3)^x

500

I bought a brand new laptop in 2020, which costed $1000. Its value has depreciated exponentially at a constant rate over time, such that if I was to sell it in 2026, it would only sell for $100. If I was to hold onto it for one more year, how much could I sell it for in 2027?

$68.13

(b=0.1^1/6=0.6813)

Solving Log Equations

100

log₄(-4x) - log₄(6) = 1

x=-6

200

log₈(5) + log₈(5x-1) = 2

x=69/25

300

Evaluate log₉1 + ln(e³)

3

400

log(x-3) - log(x) = 2

x= -1/33

500

ln(2x-7) + ln(1) = 5

x=(e⁵+7)/2

Solving Exponential Equations

100

4^2x-1 = 64

x=2

200

32^x-2 = 64

x= log₃₂64 + 2

x= 3.2

300

5*2^x +10 = 40

x= log₂6

x= 2.58

400

Evaluate log₄(1/8)

-3/2

500

5 - 2(4)^x = -17

x= log₄11

x= 1.73

Logs Word Problems

100

A town has a population of 20,000 and grows at 4% every year.  How long until the town's population reaches 28,000? 

Round to 2 decimal places.

8.58 years

200

Jenny bought a new car for $19,000.  The value of the car depreciates at 11.25% per year.  In how many years will the car be worth $10,000? 

Round to 2 decimal places.

5.38 years

300

What is the equation of the asymptote for the function y = log₂(x) + 6

x=0

400

An element with a mass of 800 grams has a half life of 5 minutes.  How long until the element decays to 10 grams.

Round to 2 decimal places.

31.61 minutes

500

A bank account with $2,000 grows continuously at a rate of 1.2% per year.  How many years until the bank account has $3,000.

Round to 2 decimal places.

33.79 years