Properties of Logarithms Check for Understanding 3103 3

Properties of Logarithms Check for Understanding – 3103. 3. 16 – Prove basic properties of logarithms using properties of exponents and apply those properties to solve problems. Check for Understanding – 3103. 3. 17 – Know that the logarithm and exponential functions are inverses and use this information to solve real-world problems.

Since logarithms are exponents, the properties of logarithms are similar to the properties of exponents.

Product Property logb mn = logb m + logb n Quotient Property logb m = logb m – logb n n Power Property logb mp = p logb m m > 0, n > 0, b ≠ 1

Use log 2 3 ≈ 1. 5850, log 2 5 ≈ 2. 3219, and log 2 7 ≈ 2. 8074 to approximate the value of each expression. 1. log 2 35 log 2 7 ∙ 5 log 2 7 + log 2 5 2. 8074 + 2. 3219 5. 1293

Use log 2 3 ≈ 1. 5850, log 2 5 ≈ 2. 3219, and log 2 7 ≈ 2. 8074 to approximate the value of each expression. 2. log 2 45 log 2 32 ∙ 5 log 2 32 + log 2 5 2 log 2 3 + log 2 5 2(1. 5850) + 2. 3219 5. 4919

Use log 2 3 ≈ 1. 5850, log 2 5 ≈ 2. 3219, and log 2 7 ≈ 2. 8074 to approximate the value of each expression. 3. log 2 4. 2 log 2 (3 ∙ 7) ÷ 5 log 2 3 + log 2 7 – log 2 5 1. 5850 + 2. 8074 – 2. 3219 2. 0705

Solve each equation. Check your solutions. 4. log 5 2 x – log 5 3 = log 5 8 log 5 = log 5 8 =8 2 x = 24 x = 12

Solve each equation. Check your solutions. 5. log 2 (x + 1) + log 2 5 = log 2 80 – log 2 4 log 2 5(x + 1)= log 2 20 5 x + 5 = 20 5 x = 15 x=3

Solve each equation. Check your solutions. 6. 3 log 2 x – 2 log 2 5 x = 2 2 100 x = x 3 log 2 x 3 – log 2 (5 x)2 = 2 0 = x 3 – 100 x 2 log 2 22 = 4= =2 2 0 = x (x – 100) 0 = x 2 0 = x – 100 x=0 x = 100

Solve each equation. Check your solutions. 7. ½ log 6 25 + log 6 x = log 6 20 8. log 7 x + 2 log 7 x – log 7 3 = log 7 72

Solve each equation. Check your solutions. 7. ½ log 6 25 + log 6 x = log 6 20 4 8. log 7 x + 2 log 7 x – log 7 3 = log 7 72 6