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

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) Log ) log 8 172

Use logarithms to solve 5) 6 3x = 816) 5 4z = 73 7).25 = log16 x

Sometimes, we can use our graphing calculators to help us solve logs 8) Solve by graphing 5 x-1 = 2 x

e The number e is a famous irrational number, and is one of the most important numbers in mathematics (we will just use 2.718)

Sometimes we use e in an exponential function. When we have base e, we use a natural logarithm (ln x) to solve. Solve 10) 18 = e 3x 11) 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?