12-3-18 AM6.1f To Simplify & Solve with Logs Got ID?  A Dog's Worst Nightmare:

Active Learning Assignment Questions?

LESSON: Law of Logarithms. If M &N are positive real numbers and b >0, ≠ 1 Exponent Rule: * The sum of the logs is the log of a product. Product Rule * The difference of the logs is the log of a quotient. Quotient Rule

* b b 2 2 Or as we have already seen: Both sides can be raised to a power, or the log of both sides can be taken. x = 4.7

A base raised to a log of itself is 1. * Power Rule Now, remember ? That’s because * * 1 5. log b b = 1 A log base of itself is 1. A base raised to a log of itself is 1. b 1 = b ?

2 2 D = {x | x > 0} -2 (x – 4) (x + 2) = 0 x = 4 or x = -2 Now, check to see if the 4 and the -2 work. -2 does not work, it would make the domain negative.

3 3 Right now, we see that “x” cannot be “1” Now, “1” wasn’t an answer, but we still need to check to see if this answer will make the domain undefined.

4 4 Right now, we see that “x” cannot be “1” Now, “1” wasn’t an answer, but we still need to check to see if this answer will make the domain undefined.

e e TRY: Solve 2 ln x = ln (2x – 1) ln x2 = ln (2x – 1) x2 = 2x – 1 Does it work? Yes!

Active Learning Assignment: (Answers) P. 202: 43a (6/5) 43b (9/2) 44a (2) 45a (5) WOW: If you are thinking of doing something stupid, don’t let fear and common sense stop you. Really?