1 / 7

3.4 Exponential and Logarithmic Equations

3.4 Exponential and Logarithmic Equations. Properties of Exp. and Log Functions. log a a x = x ln e x = x. Solving Exponential Equations. Take the ln of both sides. Ex. e x = 72. ln e x = ln 72. x = ln 72. Ex. 4e 2x = 5. Solving an Exponential Equation.

tucker-wiley
Télécharger la présentation

3.4 Exponential and Logarithmic Equations

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 3.4 Exponential and Logarithmic Equations Properties of Exp. and Log Functions • loga ax = x • ln ex = x

  2. Solving Exponential Equations Take the ln of both sides. Ex. ex = 72 ln ex = ln 72 x = ln 72 Ex. 4e2x = 5

  3. Solving an Exponential Equation First, add 4 to each side 2(32t-5) - 4 = 11 Ex. 2(32t-5) = 15 Divide by 2 (32t-5) = 15/2 ln(32t-5) = ln 7.5 (2t-5) ln3 = ln 7.5 2tln3 - 5ln3 = ln 7.5 2tln3 = 5ln3 + ln 7.5 = 3.417

  4. Ex. e2x – 3ex + 2 = 0 (ex)2 – 3ex + 2 = 0 This factors. ( ) ( ) = 0 Set both = 0 and finish solving. ex – 2 ex - 1 ex = 2 ex = 1 ln ex = ln 2 ln ex = ln 1 x = ln 2 x = 0

  5. Ex. 2x = 10 ln 2x = ln 10 x ln 2 = ln 10 Ex. 4x+3 = 7x ln 4x+3 = ln 7x (x + 3) ln 4 = x ln 7 x ln 4 + 3 ln 4 = x ln 7 Collect like terms 3 ln 4 = x ln 7 - x ln 4 Factor out an x 3 ln 4 = x( ln 7 – ln 4)

  6. Solving a Logarithmic Equation Ex. ln x = 2 Take both sides to the e eln x = e2 x = e2 Ex. 5 + 2 ln x = 4 2 ln x = -1 ln x = Ex. 2 ln 3x = 4 ln 3x = 2 3x = e2

  7. Ex. ln (x – 2) + ln (2x – 3) = 2 ln x + means mult. ln (x – 2)(2x – 3) = ln x2 e to both sides to get rid of ln’s. 2x2 – 7x + 6 = x2 x2 – 7x + 6 = 0 ( ) ( ) = 0 x – 6 x – 1 6 and 1 are possible answers Remember, can not take the log of a neg. number or zero. Put answers back into the original to check them. Notice that only 6 works!

More Related