Logarithm Practice Test
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You must show all of your work to receive credit.
Convert each logarithm into an exponent.
1.
Log28=3
2.
Logx65=4
3.
Log1/416=-2
4.
Log644=1/3
Logxy2=5
7.
Log811/9=-1/2
8.
4Log5125=12
11.
42=16
12.
1/52=1/25
15.
1/7-2=49
16.
4(3)2=36
Find the value of each logarithmic expression
17. Log525
18. Log864
19.
Log1/636
20.
Log100010
21.
Log1/497
22.
Log101/100
25.
Log51/625
26.
Log1211/11
5.
Logab=c
6.
Convert each exponent into a logarithm.
9.
35=243
10. 23=8
13.
2161/3=6
Log7343
14.
23.
25-2=1/625
Log1/31/27
24.
Use change of base to find the value of each logarithmic expression
27. Log31423
28. Log0.54241
29.
Log452.13.2
Expand each logarithm using the product and quotient rules
30. Log3(xy)
31.
32.
Log2
3(𝑥−4)
𝑎𝑏
33.
Log5(a/b)
𝑏(𝑐+𝑑)
Log73(𝑥−4)
Simplify each logarithmic expression using the product, quotient, and power rules.
34. Log3g+ Log3h
35. Log4b – Log4c
36.
3∙Loga(h)+ Loga(4-g)- b∙Loga(y)
37.
Solve each equation using your knowledge of logarithms.
38. 3x=45
39.
x∙Log2(3)- y∙ Log2(4)- z∙Log2(5)
ex=234
2
40.
5(450)x=1.7
41.
4𝑥 = 12457
42.
2x-1=3457
43.
34x+3=45x-4
Solve each exponential story problem
44. A registered Angus calf was purchased two and a 45.
half years ago for $500. This year the grown cow
was sold after gaining 29% each year. How
much was the calf sold for this year?
A Large rock on a hill loses 5% of its weight
each year due to erosion. Right now the rock
weighs 355 lbs. How long ago did the rock
weigh twice as much as it does now?
46.
A newly constructed reservoir contains can hold
up to 4,250,000 acre ft of water. If there is only
520,000 acre ft of water in the reservoir right
now and the amount of water is increasing by
27% each year, how long will it take for the
reservoir to fill up completely
47.
Right now the population of a city is 67,000. If
the number of people in the city has been
dropping 3% each year. How long ago was there
100,000 people living in the city?
48.
If a savings bond was purchased this year for
$5,000 and it is expected to increase 8.25% each
year, how long will it take for the value of the
bond to triple?
49.
Bill is working on a science project involving
bacteria growth in a Petri Dish. The particular
strain grows at 75% per hour. If there are 1000
bacteria in the dish right now, how long will it
take for the number of bacteria in the dish to
quadruple?
51.
y = –Log2x
53.
y = (3x)/25
Graph each function and its inverse
50. y = Log5x
52.
0.34-x =y
Bonus: Solve 3𝑥
2 −4𝑥+7
= 92
Answers
1) 23=8
2) x4=65
3) ¼-2=16
4) 641/3=4
5) ac=b
6) x5= y2
7) 81-1/2=1/9
8) 53=125 or 512=1254
9) Log3243=5
10) Log28=3
11) Log416=2
12) Log1/51/25=2
13) Log2166=1/3
14) Log251/625=-2
15) Log1/749=-2
16) Log39=2
17) 2
50)
Bonus: x = 3, x = 1
18) 2
19) -2
20) 1/3
21) -1/2
22) 3
23) 3
24) -2
25) -4
26) -1/2
27) 6.61
28) -8.9
29) 0.19
30) Log3x+log3y
31) Log5a- Log5b
32) Log23+ Log2(x-4)- Log2(a)-log2(b)
35) Log4(b/c)
36) Loga(h3(4-g)/yb)
37) Log2(3x/(4y5z))
38) 3.46
39) 5.49
40) -0.18
41) ±2.61
42) 12.76
43) -31.51
44) $945.03
45) 13.51 years ago
46) 8.79 years
47) 13.15 years ago
48) 13.86 years
49) 2.48 hours
33) Log7b+ Log7(c+d)- Log7(3)-log7(x-4)
34) Log3(gh)
51)
52)
53)