1. Exponents and Logarithms
Laws of
Logarithms

2. The Product and Quotient Laws
Product Law:
logb(mn) = logbm + logbn
Quotient Law:
Express
as a sum and difference of logarithms:
= log3A + log3B - log3C
Evaluate: log210 + log212.8
= log2(10 x 12.8)
= log2(128)
= log2(27)
= 7

3. Simplifying Logarithms
Solve: x = log550 - log510
x = log55
= 1
Given that log79 = 1.129, find the value of log763:
log763 = log7(9 x 7)
= log79 + log77 =
= 2.129
Evaluate: x = log45a + log48a3 - log410a4
x = 1
x = log44

4. The Power Law
Power Law:
logbmn = n logbm
Express as a single log:
= log5216

5. Applying the Power Laws
Evaluate:
= 2(1)
+ 4(1)
Given that log62 = and log65 = solve
= 0.418

6. Applying the Power Laws
Evaluate:
= 4.135
If log28 = x, express each in terms of x:
log28 = x
log223 = x
3log22 = x
a) log2512
b) log22
= log283
= 3log28
= 3x

7. Logarithm Applications
The pH of a substance is defined by the equation
pH = -log[H+], where H+ is the concentration of
hydrogen ions in moles per litre (mol/L).
Determine the pH if the hydrogen ion
concentration is mol/L.
pH = -log[H+]
= -log[1.25 x 10-5]
= -(log log10)
= -(log )
= -( )
= 4.9
Therefore, the pH is 4.9.
Note: -log = 4.9