A common logarithm has a base of 10.<br />	log 5  means log10 5<br />The log key on your calculator will find common logs....
Solve<br />Example 4-3a<br />
Solve<br />log 3x = log 17<br />x log 3 = log 17<br />x = <br />log 17log 3<br />1.23040.4771<br />=<br />= 2.5789<br />Ex...
Solve:<br />
Solve:  5x + 3 = 2x+4<br />log 5x + 3 = log 2x+4<br />(x + 3) log 5 = (x + 4) log 2<br />x log 5 + 3 log 5 = x log 2 + 4 l...
Change of base formula<br />
Find <br />Example 4-5a<br />
Find<br />Example 4-5b<br />
Quantities that grow or decay continuously can be described by a natural exponential function.<br />			f(x) = ex<br />e is...
Use a calculator to evaluate each expression to four decimal places.<br />a.<br />b.<br />Answer:1.3499<br />Answer:0.1353...
The inverse of the natural exponential function is the natural log function.<br />y = ex	      		 loge x = y<br />loge  is...
Use a calculator to evaluate each expression to four decimal places.<br />a. In 2<br />b. In <br />Answer:0.6931<br />Answ...
Write                      as a natural logarithmic equation. <br />x = loge23<br />x = ln23<br />Example 5-3a<br />
Write                                 as an exponentialequation.<br />loge x = 2.25<br />Example 5-3c<br />
Evaluate<br />Evaluate<br />Evaluate<br />Answer:<br />Answer:<br />Answer:<br />Example 5-4a<br />
Solve <br />loge 2x = 0.7<br />       2x = e0.7<br />         x = ½ e0.7<br />Answer: about 1.0069<br />Example 5-7d<br />
Solve <br />Example 5-5a<br />
Upcoming SlideShare
Loading in …5
×

Alg2 lesson 10-4 and 10-5

267 views

Published on

Published in: Education
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
267
On SlideShare
0
From Embeds
0
Number of Embeds
2
Actions
Shares
0
Downloads
0
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

Alg2 lesson 10-4 and 10-5

  1. 1. A common logarithm has a base of 10.<br /> log 5 means log10 5<br />The log key on your calculator will find common logs.<br />
  2. 2. Solve<br />Example 4-3a<br />
  3. 3. Solve<br />log 3x = log 17<br />x log 3 = log 17<br />x = <br />log 17log 3<br />1.23040.4771<br />=<br />= 2.5789<br />Example 4-3c<br />
  4. 4. Solve:<br />
  5. 5. Solve: 5x + 3 = 2x+4<br />log 5x + 3 = log 2x+4<br />(x + 3) log 5 = (x + 4) log 2<br />x log 5 + 3 log 5 = x log 2 + 4 log 2<br />x log 5 – x log 2 = 4 log 2 – 3 log 5<br />x(log 5 – log 2) = 4 log 2 – 3 log 5<br />x = 4 log 2 – 3 log 5 log 5 – log 2 <br />= 4(0.3010) – 3(0.6990) 0.6990 – 0.3010<br />= -2.244<br />
  6. 6. Change of base formula<br />
  7. 7. Find <br />Example 4-5a<br />
  8. 8. Find<br />Example 4-5b<br />
  9. 9. Quantities that grow or decay continuously can be described by a natural exponential function.<br /> f(x) = ex<br />e is a constant <br />e is approximately 2.71828<br />
  10. 10. Use a calculator to evaluate each expression to four decimal places.<br />a.<br />b.<br />Answer:1.3499<br />Answer:0.1353<br />Example 5-1c<br />
  11. 11. The inverse of the natural exponential function is the natural log function.<br />y = ex loge x = y<br />loge is usually written as ln<br />
  12. 12. Use a calculator to evaluate each expression to four decimal places.<br />a. In 2<br />b. In <br />Answer:0.6931<br />Answer:–0.6931<br />Example 5-2f<br />
  13. 13. Write as a natural logarithmic equation. <br />x = loge23<br />x = ln23<br />Example 5-3a<br />
  14. 14. Write as an exponentialequation.<br />loge x = 2.25<br />Example 5-3c<br />
  15. 15. Evaluate<br />Evaluate<br />Evaluate<br />Answer:<br />Answer:<br />Answer:<br />Example 5-4a<br />
  16. 16. Solve <br />loge 2x = 0.7<br /> 2x = e0.7<br /> x = ½ e0.7<br />Answer: about 1.0069<br />Example 5-7d<br />
  17. 17. Solve <br />Example 5-5a<br />

×