Convert
(NOT solving)
(NOT solving)
Expand/ Condense Logs
Solve for x
Graphs of logs
word problems
A=p(1 ± r)
A=p(1 ± r)
100
change to exponential: log2(8) = x
2x = 8
100
expand:
log(10)
log(5) + log(2)
100
5x = 125
3
100
Describe the transformation:
y = logb(x + 3)
horizontal shift left by 3
100
An architect is designing an apartment building where the ground floor (floor 0) is the largest. The floor space is reduced by 5.9% per floor. If the ground floor is 14,300 ft2, then which floor will have an area of 9,928.3 ft2?
6th floor
200
change to exponential: log3(1)= 0
30 = 1
200
condense:
log(a) - 3log(b)
log(a/b^3)
200
x3 = 343
x = 7
200
Describe the transformation:
y = -logb(x - 1) + 4
reflection over x-axis
horizontal shift right by 1
vertical shift up by 4
200
Your Instagram account gains followers at a rate of 5.8% per month. If you currently have 36,030 followers, when will you reach 59,846 followers?
9 months
300
change to log: 5x = 25
log525 = x
300
expand:
log(5a2b6)
log(5) + 2log(a) + 6log(b)
300
logx49 = 2
x = 7
300
what is the asymptote, domain, and range?
x = 2
domain: (2, ∞)
range: (-∞, ∞)
300
You are looking for an apartment to rent. The farther the apartment is from downtown (in miles), the cost of rent increases by 3% per mile. If the apartment you‘re looking at (0 miles from downtown) has a rent of $1830, at what mile will the rent be $2121.47?
5 miles
400
1) change to exponential: logx64 = 2
2) change to log: 3x = 27
1) x2 = 64
2) log327= x
400
condense:
log(3) + 3log(a) + 7log(b)
log(3a3b7)
400
log4(256) = x
x = 4
400
what is the asymptote, domain, and range?
x = -1
domain: (-1, ∞)
range: (-∞, ∞)
400
You work at a company that makes a certain amount of money each month. This monthly profit increases by 4.3% each month. If the company made $36,730 this month, how long will it take for the company to make $47,285 as its monthly profit?
6 months
500
1) change to exponential: logx4 = 2
2) change to log: 10x = 100
3) change to log: x5= 216
1) x2 = 4
2) log10100= x
3) logx216 = 5
500
condense:
2log(x) - 5log(y) - log(z)
log(x^2/(y^5•z))
500
log93 + log927 = x
(hint: condense first)
log981 = x
9x= 81
x = 2
500
y = log(x - 1) + 2
graph the above function and fill in the table below:
what is the asymptote, domain, and range?
x = 1, (1, ∞), (-∞,∞)
500
After lunch, you realize there are crumbs all over the floor. You vacuum the floor using multiple passes. After each pass, 15% of the crumbs are removed. If the floor had 570 crumbs at the start, how many passes of the vacuum will it take for 215 of the crumbs to be left?
6 passes