Properties of Logarithms

Use log₁₀ 5 ≈ 0.6990 and log₁₀ 7 ≈ 0.8451 to approximate the value of each expression. 1. log₁₀ 25 = _______

• 1.3980

• 0.8451

• 1.6990

• 0.6990

Use log₁₀ 5 ≈ 0.6990 and log₁₀ 7 ≈ 0.8451 to approximate the value of each expression. 2. log₁₀ 175 = _______

• 2.2431

• 1.5441

• 2.0000

• 1.6990

Solve each equation. Check your solutions. 3. log₈ 48 − log₈ w = log₈ 4. Solve for w.

• w = 12

• w = 8

• w = 6

• w = 16

Solve for x in the equation 4 log₂ x + log₂ 5 = log₂ 405.

• x = 3

• x = 5

• x = 9

• x = 4

Solve for d in the equation log₂ d = 5 log₂ 2 − log₂ 8.

• d = 4

• d = 8

• d = 16

• d = 2

Solve each equation. Check your solutions. 6. log₁₀ (3m − 5) + log₁₀ m = log₁₀ 2. Solve for m.

• m = 1

• m = 2

• m = 3

• m = 5

Solve for b in the equation log₁₀ (b + 3) + log₁₀ b = log₁₀ 4.

• b = 1

• b = 2

• b = 4

• b = 0

Solve each equation. Check your solutions. 8. log₈ (t + 10) − log₈ (t − 1) = log₈ 12. Solve for t.

• t = 2

• t = 4

• t = 6

• t = 8

Solve for a in the equation log₃ (a + 3) + log₃ (a + 2) = log₃ 6.

• a = 1

• a = 2

• a = 0

• a = -1

Solve for w in the equation log₁₀ 4 + log₁₀ w = 2.

• w = 25

• w = 5

• w = 20

• w = 10