Ap Pre-Calculus Unit 2B: Logs & Exps

How do you do a log on a calculator?

math→ log base

What is the rule with domains and ranges of logs & exponentials since they are inverses?

The domain and range are switched

Domain of Exp/Range of Log: (-∞,∞)

Range of Exp/Domain of Log: (0,∞)

What does a graph of exponential growth look like

b>1 (the base is greater than 1)

What graph of an exponential decay look like?

0<b<1 (the base is a decimal, between 0 & 1)

What does the graph of a logarithmic growth look like?

b>1 (base is greater than 1)

What does a graph of logarithmic decay look like?

0<b<1 (the base is a decimal, between 0 & 1)

What are the asymptotes of log and exponential functions?

Log: x=0

Exp: y=0

What are the x and y intercepts of logs and exponentials?

Logs: y= none, x=(1,0)

Exponential: y=(0,1), x=none

Describe logarithmic and exponentials on a table

Logs:

• x-values: common ratio

• y-values: equal length

Exp:

• x-values: equal length

• y-values: common ratio

How can you check if a log & exp are inverses of one another?

By turning them into composition functions & getting x

What is the product property of logarithmic functions?

What is the quotient property of logarithmic functions?

What is the power property of logarithmic functions?

What is the change of base formula?

If loga(B)=loga(C)..

B=C

• you can cancel the logs on on both sides, since they have the same base

• set b & c equal and solve!

How do you solve a log inequality?

1. There is a restriction in logs where the argument has to be x>0

2. So set the arguments as (argument)<0

3. Solve the inequality and see where they intersect

4. That’s your answer

How do you solve an exponential inequality?

Normally, since there are no restrictions

What are semi log plots?

One axis is scaled using logs and the other is not

• 1-10 (each line is 1)

• 10-100 (each line is 10)

• 100-1000 (each line is 100)

How do exponential functions appear on semi log graphs?

They appear linearly