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:
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