1. Logarithms Laws (Unity)
loga a = 1
Example: log88
= log8 81
y = 81
a = 8
= 1
x = x
y = ax
81 = 8x
x = 1

2. Logarithms Laws (Multiplication)
loga(xy) = logax + logay
Example: log327 + log33
= log3 (27 x 3)
y = 34
a = 3
= log3 81
x = x
= log3 34
y = ax
= 4
34 = 3x
x = 4

3. Logarithms Laws (Division)
loga(x/y) = logax - logay
Example: log327 - log33
= log3 (27 ÷ 3)
y = 32
a = 3
= log3 9
x = x
= log3 32
y = ax
= 2
32 = 3x
x = 2

4. Logarithms Laws (Powers)
loga xn = n logax
Example: log381
= log3 34
y = 31
a = 3
= 4 log33
x = x
= 4 x 1
y = ax
= 4
31 = 3x
x = 1

5. Logarithms Laws (Examples)
Given log53 = 0.68 and log54 = 0.86
1) log512
2) log50.75
= log5(3x4)
= log5(3÷4)
= log53 + log54
= log53 - log54 = =
= 1.54
= -0.18

6. Logarithms Laws (Examples)
Given log53 = 0.68 and log54 = 0.86
3) log59
4) log520
= log5(3x3)
= log5(5x4)
= log53 + log53
= log55 + log54
Exercise 4.5 (page 143) = =
= 1.36
= 1.86