Flashback 9-20-12 An industrial cleaner is manufactured using only the 3 secret ingredients A, B, and C, which are mixed in the ratio of 2:3:5, respectively, by weight. How many pounds of secret ingredient B are in a 42-pound (net weight) bucket of this cleaner? A.   4.2 B. 12.6 C. 14.0 D. 18.0 E. 21.0 If n = 8 and 16*2m = 4n-8, then m = ? F. –4 G. –2 H.   0 J.   1 K.   8

He wears glasses during math… Joke of the day He wears glasses during math… 

because it improves division.

What is the inverse of exponential functions? Base a: alogax = x logaax = x for a>1, x>0 Base e: eln x = x ln ex = x for x>0

Let’s use it ln x = 3t + 5 e2x = 10

Properties of Logarithms Product Rule: logaxy = logax + logay Quotient Rule: loga(x/y) = logax - logay Power Rule: logaxy = ylogax Change of base: logax = ln x/ln a

Examples See worksheet. log (3 *2^3) = log 3 + log 2^3 = log 3 + 3 log 2 Log u4/v = Log u4 – log v = 4 log u – log v 4log 3 - 4 log 8 = log 34 – log 84 = log (34 / 84)

Example P. 42 example 6 Compound interest formula: A = P(1+r)t

Class/homework Complete worksheet

Exit Slip 1. Which of the following is a solution to 2 – 3-x = - 1 ? x = - 2 b. x = - 1 c. x = 0 d. x = 1 e. There are no solutions