Logarithms Test — 10 Questions

Question 1

Compute log_2 8.

Accepted Answer

2^3 = 8, so log_2 8 = 3.

Answer

2

Answer

3

Answer

4

Answer

8

Question 2

Compute log_3 81.

Accepted Answer

3^4 = 81, so log_3 81 = 4.

Answer

2

Answer

3

Answer

4

Answer

9

Question 3

Compute log_5 (1)/(25).

Accepted Answer

(1)/(25) = 5^-2, so log_5 (1)/(25) = -2.

Answer

-2

Answer

-1

Answer

1

Answer

2

Question 4

Using log_a(xy) = log_a x + log_a y, compute log_2(4 · 8).

Accepted Answer

log_2(4 · 8) = log_2 4 + log_2 8 = 2 + 3 = 5. (Check: 4 · 8 = 32 = 2^5.)

Answer

3

Answer

5

Answer

6

Answer

32

Question 5

Compute log_3 27 - log_3 3.

Accepted Answer

log_3 27 = 3 and log_3 3 = 1, so the difference is 2. Equivalently, log_3 (27)/(3) = log_3 9 = 2.

Answer

1

Answer

2

Answer

3

Answer

9

Question 6

Compute log_2(2^10).

Accepted Answer

By the identity log_a(a^k) = k, log_2(2^10) = 10.

Answer

2

Answer

5

Answer

10

Answer

1024

Question 7

Solve for x: log_2 x = 4.

Accepted Answer

log_2 x = 4 ⇔ x = 2^4 = 16.

Answer

2

Answer

8

Answer

16

Answer

32

Question 8

If log_a 5 = 2, what is a? (Assume a > 0, a ≠ 1.)

Accepted Answer

log_a 5 = 2 ⇔ a^2 = 5 ⇔ a = √(5) (since a > 0).

Answer

√(5)

Answer

2

Answer

5

Answer

25

Question 9

Solve for x: log_2(x) + log_2(x-2) = 3.

Accepted Answer

Combine: log_2(x(x-2)) = 3 ⇒ x^2 - 2x = 8 ⇒ x^2 - 2x - 8 = 0 ⇒ (x-4)(x+2) = 0. Domain requires x > 2, so x = 4.

Answer

x = 2

Answer

x = 4

Answer

x = 6

Answer

x = 8

Question 10

Compute log_10 1000 + log_10 0.01.

Accepted Answer

log_10 1000 = 3 and log_10 0.01 = -2. Sum: 3 + (-2) = 1. (Or: log_10(1000 · 0.01) = log_10 10 = 1.)

Answer

0

Answer

1

Answer

2

Answer

5

Logarithms Test — 10 Questions

Logarithm properties — quick reference

Logarithms Test — 10 Questions

Logarithm properties — quick reference