1. Logarithmic Functions
5.5

2. Logarithms to other bases
logb x = a if and only if x = ba.
Note: b > 0, and b ≠ 1
The common logarithm of any positive real number x is defined to be the exponent you get when you write x as a power of 10.
log x = a IFF x = 10a
This is true because log has a base of 10, however, we do not write it the same way we don’t write x = 1x.
For example: log 6.3 ≈ 0.8 because 6.3 ≈ 100.8
Logarithms to other bases

3. Find the decibel level for each sound with the given intensity I of an average car at 70 km/h, I = 106.8I0.
Find the decibel level of two stereos, playing the same music simultaneously at 62dB.
Ex. 1 & 2

4. Ex. 3 Write each equation in exponential form.
A) log4 16 = 2
B) log 1000 = 3 C)
Ex. 3 Write each equation in exponential form.

5. Natural Logarithm Function
ln x = k IFF ek = x
**NOTE** The ln eliminates e and vice versa
Natural Logarithm Function

6. Ex. 4 Find the value of x to the nearest hundredth.
A) 10x = 100
B) ex = 100
Ex. 4 Find the value of x to the nearest hundredth.

7. Ex. 5 Find each logarithm. (Do not use a calculator)
A) log 100
B) log 0.01
C) log3 9
D) log5
E) ln e2
F) log5 58
Ex. 5 Find each logarithm. (Do not use a calculator)

8. Ex. 6 Given log 4.17 ≈ 0.6201, find (w/o a calc):
HINTS
Put given in exp. form & think match
You can also match and substitute
Use properties of logs
C) log
log4.17-1
-1log4.17
-1(.6201)
-.6201
A) log 417
log(4.17102)
log( 102)
log( )
2.6201
B) log 0.417
4.17 (given exp. form)
(10-1) 4.17 (10-1)
.417  (matches)
log ( ) (plug in)
-.3799
Ex. 6 Given log 4.17 ≈ , find (w/o a calc):

9. Ex. 7 Solve for x without using a calculator.
A) log x = 3
B) log | x | = 3
C) log | x – 1 | = 3
D) log 4 x = 1.5
E) ln x = 1.5
F) ln x = 0
Ex. 7 Solve for x without using a calculator.

10. Ex. 8 Solve for x using a calculator.
A) log x = 0.7
B) ln x = –1.5
C) ex = 5
Ex. 8 Solve for x using a calculator.