1.
Simplify: logₐ(a³).
2.
If log₃(x) = 4, then x = ?
3.
What is the scientific notation for 0.000890?
A
8.90 × 10⁻⁴
B
8.90 × 10⁴
C
89.0 × 10⁻⁵
D
0.89 × 10⁻³
4.
Write 1.23 × 10⁻² in standard notation.
A
0.0123
B
123
C
0.123
D
1230
5.
Using the change of base formula, log₅(20) can be written as:
A
log₁₀(5) / log₁₀(20)
B
log₁₀(20) / log₁₀(5)
C
log₂₀(5) / log₂₀(10)
D
log₅(10) / log₂₀(10)
6.
What is the value of log₂(√8)?
7.
Write 3.2 × 10⁵ in standard notation.
A
320000
B
32000
C
0.000032
D
3200
8.
The logarithm of a number to its own base is always:
A
0
B
1
C
The number itself
D
Undefined
9.
What is the value of log₆(216)?
10.
Which law states that logₐ(x/y) = logₐ(x) - logₐ(y)?
A
Product rule
B
Quotient rule
C
Power rule
D
Change of base rule
11.
If log₁₀(2) = 0.3010, what is log₁₀(200)?
A
1.3010
B
2.3010
C
3.3010
D
0.3010
12.
Simplify: log₃(81) - log₃(9).
13.
Which of the following is the logarithmic form of 5³ = 125?
A
log₅ 125 = 3
B
log₃ 125 = 5
C
log₁₂₅ 5 = 3
D
log₅ 3 = 125
14.
The scientific notation of 450000 is:
A
4.5 × 10⁵
B
45 × 10⁴
C
4.5 × 10⁶
D
0.45 × 10⁶
15.
What is the value of log₁₀(1)?
16.
The number 93000000 in scientific notation is:
A
9.3 × 10⁷
B
93 × 10⁶
C
9.3 × 10⁸
D
0.93 × 10⁸
17.
Convert 4.56 × 10³ to standard notation.
A
4560
B
456
C
0.00456
D
45600
18.
What is the value of logₑ(e²)?
19.
What is log₁₀(10⁵)?
20.
What is the value of logₕ(1) for any base h>0, h≠1?