Download presentation

Presentation is loading. Please wait.

1
**7-5 Logarithmic & Exponential Equations**

2
**Terms and Concepts these will be on a quiz**

3
**Write original equation.**

EXAMPLE 1 Solve by equating exponents Solve 4 = x 1 2 x – 3 SOLUTION 4 = x 1 2 x – 3 Write original equation. Rewrite 4 and as powers with base 2. 1 2 (2 ) = (2 ) 2 x – 3 x – 1 2 = 2 2x – x + 3 Power of a power property 2x = –x + 3 Property of equality for exponential equations x = 1 Solve for x. The solution is 1. ANSWER

4
**GUIDED PRACTICE for Example 1 Solve the equation. 3. 81 = 1 3**

= 3 – x 1 3 5x – 6 = 27 2x x – 1 SOLUTION –3 SOLUTION –6 = 1000 7x + 1 3x – 2 – 8 5 SOLUTION

5
**Write original equation.**

EXAMPLE 2 Take a logarithm of each side Solve 4 = 11. x SOLUTION 4 = 11 x Write original equation. log 4x = log 4 11 4 Take log of each side. 4 log 4 x = log b = x b x x = log 11 log 4 Change-of-base formula x Use a calculator. The solution is about Check this in the original equation. ANSWER

6
**GUIDED PRACTICE for Examples 2 and 3 Solve the equation. 4. 2 = 5**

= 5 x SOLUTION about 2.32 = 15 9x SOLUTION about

7
**Terms and Concepts these will be on a quiz**

8
**Solve a logarithmic equation**

EXAMPLE 4 Solve a logarithmic equation Solve log (4x – 7) = log (x + 5). 5 SOLUTION log (4x – 7) = log (x + 5). 5 Write original equation. 4x – 7 = x + 5 Property of equality for logarithmic equations 3x – 7 = 5 Subtract x from each side. 3x = 12 Add 7 to each side. x = 4 Divide each side by 3. The solution is 4. ANSWER

9
**Exponentiate each side of an equation**

EXAMPLE 5 Exponentiate each side of an equation Solve (5x – 1)= 3 log 4 SOLUTION (5x – 1)= (5x – 1)= 3 log 4 Write original equation. 4log4(5x – 1) = 4 3 Exponentiate each side using base 4. b = x log b x 5x – 1 = 64 5x = 65 Add 1 to each side. x = 13 Divide each side by 5. The solution is 13. ANSWER

10
**Solve the equation. Check for extraneous solutions.**

GUIDED PRACTICE for Examples 4, 5 and 6 Solve the equation. Check for extraneous solutions. 7. ln (7x – 4) = ln (2x + 11) 9. log 5x + log (x – 1) = 2 SOLUTION 5 SOLUTION 3 8. log (x – 6) = 5 2 log (x + 12) + log x =3 4 SOLUTION 4 SOLUTION 38

Similar presentations

© 2023 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