February 27, 2012At the end of today, you will be able use log properties to solve exponential equations with different bases.Warm-up: Correct Unit 3 Review Pt. 1 Pg. 271 #11, 13,

23, 25, 39, 41, 45, 71, 73, 79-83 odd11. Right 1 41. log464 = 3 83. 2ln x + 2ln y + lnz

13. Reflect over x-axis, 45. 3left 2 71. 1.58523. X = -4 73. -2.32225. X = 22/5 79. 1 + 2log5x

39. a) $1,069,047.14 81. 1 + log3 2 – 1/3log3 x

b) 7.9 years *Finals in 17 school days!*Spring break in 22 school days!

Expressing logs as a common log

We can express logs with different bases and change it to the common log.

Change of Base Formula or

Example 1:

11log3

loga n logn

loga

Try: log7 18

loga n lnn

lna

3log

11log183.2

Using logs to solve exponential equations

Example 2: Solve 4x = 19 log4 4x = log4 19

x log4 4 = log4 19

x = 2.1240

1. When you can’t get the same base, log both sides with the same base.

2. Use the power property to rewrite 4x.

3. Use the change of base formula to find x.

x(1) = log4 19

* Remember the properties:• loga a = 1 • ln e = 1

x log19

log4

Practice

1. 6x = 40

2. en+2 = 3

1. When you can’t get the same base, log both sides with the same base.

2. Use the power property to rewrite .

3. Use the change of base formula to find x.

In exponential word problems, they usually give you the formula.Just make sure you understand what is asking for!

Example 1:A youtube video has the number y of hits each month

and can be modeled by y = 4080ekt, where t represents the number of months the website has been operating. In the video’s third month, there were 10,000 hits. Find the number of k, and use this result to predict the number of hits it will receive after 24 months.

Example 2

The number N of bacteria in your backpack is modeled by N = 100ekt, where t is the time in hours. If N = 300 when t = 5, estimate the time required for the population to double in size.

CW 3.4b: Pg. 254 #25-55odd, Pg. 266 #38, 40

Unit 3 Review HW: Pg. 272 #85-93, 97-113, 119-129, 145 ALL ODDS