LOGARITHMS

1

What is the value of log₁₀(1000)?

A 1 B 2 C 3 D 4

2

Simplify log₂(16) + log₂(2).

A 5 B 4 C 6 D 3

3

What is the value of log₄(64)?

A 2 B 3 C 4 D 8

4

Simplify log₁₀(100) - log₁₀(10).

A 1 B 2 C 10 D 0

5

Which of the following is equal to logₐ(m) + logₐ(n)?

A logₐ(mn) B logₐ(m/n) C logₐ(mⁿ) D logₐ(m+n)

6

The scientific notation of 0.0000081 is:

A 8.1 × 10⁻⁶ B 81 × 10⁻⁷ C 8.1 × 10⁻⁷ D 0.81 × 10⁻⁵

7

Simplify: logₕ(hⁿ) for h>0, h≠1.

A n B hⁿ C 1 D 0

8

Which of the following is the correct way to write 0.00056 in scientific notation?

A 5.6 × 10⁻⁴ B 5.6 × 10⁴ C 56 × 10⁻⁵ D 0.56 × 10⁻³

9

The number 93000000 in scientific notation is:

A 9.3 × 10⁷ B 93 × 10⁶ C 9.3 × 10⁸ D 0.93 × 10⁸

10

Convert 6.02 × 10²³ to standard notation.

A 602000000000000000000000 B 60200000000000000000000 C 0.000000000000000000000602 D 6020000000000000000000

11

What is log₂(0.5) equal to?

A 1 B -1 C 0.5 D -0.5

12

What is the base of a common logarithm?

A 2 B e C 10 D 1

13

What is the characteristic of log₁₀(0.0045)?

A -2 B -3 C 2 D 3

14

Express 0.0000072 in scientific notation.

A 7.2 × 10⁻⁶ B 7.2 × 10⁶ C 72 × 10⁻⁷ D 0.72 × 10⁻⁵

15

If log₁₀(5) = 0.6990, what is log₁₀(50)?

A 0.6990 B 1.6990 C 2.6990 D 3.6990

16

Which of the following is equivalent to logₐ(m)ⁿ?

A n logₐ(m) B logₐ(m) + n C logₐ(m/n) D logₐ(m) - n

17

The scientific notation of 450000 is:

A 4.5 × 10⁵ B 45 × 10⁴ C 4.5 × 10⁶ D 0.45 × 10⁶

18

What is logₐ(a²)?

A 2 B a C 2a D 1

19

What is the value of log₂(32) - log₂(4)?

A 3 B 4 C 5 D 2

20

What is the value of log₂(128)?

A 6 B 7 C 8 D 9

21

If logₐ(x) = logₐ(y), then:

A x = y B x ≠ y C x = 1 D y = 1

22

If log₁₀(2) = 0.3010, what is log₁₀(200)?

A 1.3010 B 2.3010 C 3.3010 D 0.3010

23

The standard notation of 5.67 × 10⁰ is:

A 5.67 B 567 C 0.567 D 5670

24

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)

25

Which of the following is equal to log₂(8) × log₃(9)?

A 6 B 9 C 12 D 18