common logarithms

Day 3Common

Logarithms

Express each number using exponents.

OA. 36 G. 1OB. 121 What about . . .OC. 4 H. 345OD. I. 0.0023

OE. 100OF. 1000

Logarithms give you a way to solve for an exponent.

OEx: 5x = 12

Common Logarithms are any logarithm of base 10

Ex: log10 or log

Rewriting: 10b = a log10a=b

A. 102 = 100

B. 33 = 27

C. 25 = 32

log10 100 = 2

log3 27 = 3

log2 32 = 5

E. 641/2 = 8

F. log6 36 = 2

Log64 8 = 1/2

D. 9-2 = 1 81

G. log3 81 = 4

H. log14 = -2 1 196

I. log10 10 = 1

J. Log 1 = 0

Log9 = -2 1 81

62 = 36

34 = 81

101 = 10

100 = 1

14-2 = 1 196

Evaluate without a calculator:A. Log4 64

Step 1: set = to x Log4 64 = x

Step 2: rewrite in exp. form

4x = 64

Step 3: break down the #’s

22x = 26

Step 4: once the bases are the same, set exp. =

2x = 6

x = 3

B) Log5 125

5x = 125

5x = 55

x = 5

C) Log4 16

4x = 16

22x = 24

2x = 4

x = 2

D) Log343 7

343 = 7x

73x = 71

x = 1/3

Log343 7 = x

3x = 1

E) Log3

3x = 3-5

Log3 = x

x = -5

243 1

3x = 243 1

2431

Evaluate using a calculator.

A) Log 75 1.8751

B) Log -3 Not possible

** log10 (-3) = x

10x = -3

C) Log 1 0

** log10 1= x 10x = 1

But what if the base isn’t 10?Use Change of Base Formula:

logb a = or

A) log5 3 log 3log 5

= 0.6826

B) log11 18 log 18log 11

= 1.2054

C) log4 8 log 8log 4 = 1.5