1. Warm Up – 4/23 - Wednesday
1. Sketch the following function and state the range.
𝑦=−2∙ 3 −𝑥 −1
2. Edward deposits $400 into bank with an interest rate of 5%. Find the amount he has at the end of 1 year if the bank compounds A) Quarterly B) Monthly
C) Daily D) Continuously

2. Compounding Continuously Classwork

3. Logarithms Intro
How would I solve this equation?
3 𝑥 =5

4. Logarithms
In order to solve equations like that we have to define what is called a logarithm or a log.
A log is just the inverse of an exponential function.
Exponential Form: 𝑦= 𝑏 𝑥
Log Form: log 𝑏 𝑦 =𝑥
These two forms mean the same thing!

5. Things you will hear Mr. Gill say…
“The base is the base…”
Meaning
3 𝑥 =5
the base of an exponential – “3 to the X”
log =𝑥
becomes the base of the log – “log base 3”

6. Things you will hear Mr. Gill say…
“The exponent goes all by itself
Meaning
3 𝑥 =5
The exponent – “X”
log =𝑥
Ends up all by itself on the other side of the log

7. Writing Exponentials as Logs
Convert from Exponentials to Logs
3 𝑥 = 𝑥+1 =9
Convert from Logs to Exponentials
3. log =𝑥 log =𝑦

8. Base 10 and “Log Naturale”
A log without a base is log base 10.
log 10 𝑥 = log 𝑥
Anything written as "𝑙𝑛“ is the natural log or “log base e.”
log 𝑒 𝑥 = ln 𝑥
You will find both log base 10 and “ln” on your calculator.

9. Solving Simple Logs What is the value of log 2 4 ?
All this is asking is “what is the exponent that I raise the base to get the number inside?”
In other words 2 to what power gives me 4?
2 2 =4 therefore log 2 4 =2.

10. Simple Logs continued
log
log
log

11. Simple Logs continued log 5 125 =3. Fairly straightforward: 5 3 =125.
Remember whenever you have a fraction that comes from a negative exponent. 3 −1 puts the three in the denominator. 3 −1 = 1 3

12. Simple Logs Continued log 2 1 4 =−2 .
This follows the same logic as the previous example. The negative puts the answer in the denominator and then I square it.
2 −2 = = 1 4 .