CK-12-Pre-Calculus Concepts

http://www.ck12.org Chapter 3. Logs and Exponents

(bw)n=bw·n
There are a few standard results that should be memorized and should serve as baseline reference tools.

• logb 1 = 0


• logbb= 1


• logb(bx) =x


• blogbx=x

Example A
Simplify the following expressions:

a. log 464

b. log 1232

c. log 335

d. log 2128

Solution:

a. log 464 =log 443 = 3 ·log 44 = 3 · 1 = 3

b.

log 1232 =xcan be rewritten as

( 1

2

)x

= 32.

2 −x= 32

x=− 5

c. log 335 = 5 ·log 33 = 5

d. log 2128 =log 227 = 7

Example B
Write the expression as a logarithm of a single argument.
log 212 +log 46 −log 224
Solution: Note that the center expression is of a different base. First change it to base 2 by switching back to
exponential form.

log 46 =x↔ 4 x= 6

22 x= 6 ↔log 26 = 2 x

x=^12 log 26 =log 2612

Thus the expression with the same base is:

log 212 +log 2612 −log 224 =log 2

(

12 ·√ 6

24

)

=log 2

(√

6

2

)