Everything Maths Grade 12

2.4 CHAPTER 2. LOGARITHMS

Activity: Change of Base

Change the following tothe indicated base:

1. log 2 (4) to base 8


2. log 10 (14) to base 2


3. log 16 (4) to base 10


4. logx(8) to base y


5. logy(x) to base x

See video: VMgiq at http://www.everythingmaths.co.za

2.4 Laws of Logarithms EMCE

Just as for the exponents, logarithms have somelaws which make working with them easier. These

laws are based on the exponential laws and are summarised first and thenexplained in detail.

loga(1) = 0 (2.4)

loga(a) = 1 (2.5)

loga(x.y) = loga(x) + loga(y) (2.6)

loga

�

x

y

�

= loga(x)− loga(y) (2.7)

loga(xb) = b loga(x) (2.8)

loga

�√b

x

�

=

loga(x)

b

(2.9)

2.5 Logarithm Law 1: log

a

1=0 EMCF

Since a^0 = 1

Then, loga(1) = 0 by definition of logarithm in Equation 2.

For example,

log 2 1 = 0

and

log 25 1 = 0

Activity: Logarithm Law 1:loga1=