1. Good afternoon Happy Thursday!!! Warm UP:
Convert from logs to exponentials or vice versa
1) log 2 𝑥−2 =18
2) 𝑒 𝑥 =20
Solve by changing the bases:
2 𝑥+4 =32
1 9 𝑥−5 =27

2. Law of Logs

3. Review laws of exponents
𝑥 𝑛 ∗ 𝑥 𝑚 = 𝑥 𝑛+𝑚
𝑥 𝑛 𝑥 𝑚 = 𝑥 𝑛−𝑚
𝑥 𝑛 𝑚 = 𝑥 𝑛∗𝑚
𝑥𝑦 𝑛 = 𝑥 𝑛 ∗ 𝑦 𝑛 𝑎𝑛𝑑 𝑥 𝑦 𝑛 = 𝑥 𝑛 𝑦 𝑛
𝑥 −𝑛 = 1 𝑥 𝑛 and 𝑥 −𝑛 = 𝑥 𝑛

4. Law of Logs
Just like with Exponent Laws(rules) Logs Rules can change the look of a logarithm

5. Multiplication
log 𝑏 𝑀𝑁= log 𝑏 𝑀 + log 𝑏 𝑁 Similar to : Product Rule Ex: log 2 4𝑥 = log 2 4+ log 2 𝑥

6. Division log 𝑏 𝑀 𝑁 = log 𝑏 𝑀 − log 𝑏 𝑁 Similar to Quotient Rule
Ex: log 2𝑥 5 = log 2𝑥 −𝑙𝑜𝑔5

7. Power Rule log 𝑏 𝑀 𝑥 =𝑥𝑙𝑜 𝑔 𝑏 𝑀 Ex: log (10 2 ) =2 log 10
Test this one to be sure:

8. Logical Rules 𝐿𝑜 𝑔 𝑏 𝑀=𝐿𝑜 𝑔 𝑏 𝑁 if and only if 𝑀=𝑁 log b 𝑏 =1

9. Try it
Confirm the equations are true log 10 =1 log 1 =0 𝑙𝑛 20 = ln 20

10. Practice: Write each log in expanded form log 5 (𝑥𝑦) log 5 𝑥 𝑦 2

11. More Practice Write each as single log. log 𝑥+ log 𝑦− log 𝑧 =
2𝑙𝑛𝑥+𝑙𝑛𝑦=
2 log 𝑥+3 log 𝑦+2 log 𝑧 =
1 2 ln 𝑥 −( 1 3 ) ln 𝑦 =

12. Homework
Pg 405 #’s odd,
Pg #’s 1-8, 35-38