11-5 Common Logs and Natural Logs. Any log that has base 10 is called a common logarithm. We usually do not write the 10. We can figure out many common logs easily Ex) log 100 =2 log 1000= 3. You can apply all properties to common logs. You can use a calculator to help. Evaluate:
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.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
Sometimes, we can’t evaluate logs in our heads. Then, we use the change of base formula to help.
Use change of base to evaluate:
3) Log91043 4) log8 172
Use logarithms to solve use the change of base formula to help.
5) 63x = 81 6) 54z = 73
7) .25 = log16x
8) Solve by graphing 5x-1 = 2x
e solve logs
The number e is a famous irrational number, and is one of the most important numbers in mathematics.
(we will just use 2.718)
Calculating Interest solve logs
Simple Interest Continuously Compounded
A= total, P = initial amount (principal)
r= rate n=times compounded t=time
Sometimes we use e in an exponential function. When we have base e, we use a natural logarithm (ln x) to solve.
10) 18 = e 3x11) 4.5 > e .031x
In a study at White Oak, scientist found that time t=0, 5% of people have heard a rumor. After 2 days, 25% of students heard that rumor. How long will it take for 80% of White Oak Students to hear that rumor?
13) Convert of people have heard a rumor. After 2 days, 25% of students heard that rumor. How long will it take for 80% of White Oak Students to hear that rumor?log6 254 to a natural log, then evaluate.
14) Solve 6.5 = -16.25 lnx
15) Solve 48