Everything Maths Grade 12

CHAPTER 2. LOGARITHMS 2.10

3 log 3 + log 125 = 3 log 3 + log 5^3

= 3 log 3 + 3 log 5∵ loga(xb) = b loga(x)

= 3 log 15 (Logarithm Law 3)

Step 3 : Final Answer

We cannot simplify anyfurther. The final answer is:

3 log 15

Example 2: Simplification of Logs

QUESTION

Simplify, without use ofa calculator:

8

(^23)

• log 232
  SOLUTION
  Step 1 : Try to write any quantities as exponents
  8 can be written as 23. 32 can be written as 25.
  Step 2 : Re-write the question using the exponential forms of the numbers
  8
  (^23)


• log 2 32 = (2^3 )
  (^23)


• log 225
  Step 3 : Determine which lawscan be used.
  We can use:
  loga(xb) = b loga(x)
  Step 4 : Apply log laws to simplify
  (2^3 )
  2
  (^3) + log 225 = (2)^3 ×
  2
  (^3) + 5 log 22
  Step 5 : Determine which lawscan be used.
  We can now use logaa = 1
  Step 6 : Apply log laws to simplify
  (2)^2 + 5 log 2 2 = 2^2 + 5(1) = 4 + 5 = 9
  Step 7 : Final Answer
  The final answer is:
  8
  2
  (^3) + log 2 32 = 9