1. Log Functions
Unit 3

2. What’s a Log?
The logarithmic function is the inverse of an exponential function.
Therefore, a log is an exponent. (just like diving is multiplying by a fraction)

3. Log form Exponential Form

4. The Base of a Log (the calculator only does log and ln…)
b, the base of a log, can be any number…
For example, log3 9 = ?
log6 216 = ?
(the calculator only does log and ln…)

5. The Base of a Log These bases are frequently used:
Common log – if the base is not written, it is base 10
Natural log (ln) has a base of e
Remember e is an irrational number with a value of approx

6. Characteristics of Log Functions
Generally, for b > 0, b ≠ 1, x > 0…
logb 1 = (because…)
logb b = 1
logb bx = x
b logb x = x

7. Characteristics of Common Log Functions
For base 10 common logs, x > 0
log 1 = (because…)
log 10 = 1
log 10x = x
10 log x = x

8. Characteristics of Natural Log Functions
For base e natural logs, x > 0
ln 1 = (because…)
ln e = 1
ln e x = x
e ln x = x

9. Properties of logarithms
Product: logb RS = logb R + logb S
Quotient: logb R = logb R – logb S S
Power: logb Rc = c logb R

10. Change of Base Formula
Here’s how we can use the calculator to evaluate log34 !!
logb x = log x
log b
So, log34 = ?