Download presentation

Presentation is loading. Please wait.

1
**Properties of Logarithms**

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

2
Since logarithms are exponents, the properties of logarithms are similar to the properties of exponents.

3
**n 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 > 0, b ≠ 1

4
Use log2 3 ≈ , log2 5 ≈ , and log2 7 ≈ to approximate the value of each expression. log2 35 log2 7 ∙ 5 log2 7 + log2 5 5.1293

5
**2. log2 45 log2 32 ∙ 5 log2 32 + log2 5 2log2 3 + log2 5**

Use log2 3 ≈ , log2 5 ≈ , and log2 7 ≈ to approximate the value of each expression. 2. log2 45 log2 32 ∙ 5 log log2 5 2log2 3 + log2 5 2(1.5850) 5.4919

6
**3. log2 4.2 log2 (3 ∙ 7) ÷ 5 log2 3 + log2 7 – log2 5**

Use log2 3 ≈ , log2 5 ≈ , and log2 7 ≈ to approximate the value of each expression. 3. log2 4.2 log2 (3 ∙ 7) ÷ 5 log2 3 + log2 7 – log2 5 – 2.0705

7
**4. log5 2x – log5 3 = log5 8 log5 = log5 8 = 8 2x = 24 x = 12**

Solve each equation. Check your solutions. 4. log5 2x – log5 3 = log5 8 log = log5 8 = 8 2x = 24 x = 12

8
**5. log2 (x + 1) + log2 5 = log2 80 – log2 4 log2 5(x + 1)= log2 20**

Solve each equation. Check your solutions. 5. log2 (x + 1) + log2 5 = log2 80 – log2 4 log2 5(x + 1)= log2 20 5x + 5 = 20 5x = 15 x = 3

9
**3log2 x – 2log2 5x = 2 100x2 = x3 log2 x3 – log2 (5x)2 = 2**

Solve each equation. Check your solutions. 3log2 x – 2log2 5x = 2 log2 x3 – log2 (5x)2 = 2 100x2 = x3 0 = x3 – 100x2 0 = x2(x – 100) 0 = x = x – 100 log = 2 22 = x = x = 100 4 =

10
**½ log6 25 + log6 x = log6 20 8. log7 x + 2log7 x – log7 3 = log7 72**

Solve each equation. Check your solutions. ½ log log6 x = log6 20 8. log7 x + 2log7 x – log7 3 = log7 72

11
**½ log6 25 + log6 x = log6 20 4 log7 x + 2log7 x – log7 3 = log7 72 6**

Solve each equation. Check your solutions. ½ log log6 x = log6 20 4 log7 x + 2log7 x – log7 3 = log7 72 6

Similar presentations

© 2019 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google