Everything Maths Grade 12

2.10 CHAPTER 2. LOGARITHMS 2.10 Logarithm Law 6: loga( b √ x)= loga(x) b EMCK The derivation of this law is identical to the der ...

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 ...

2.11 CHAPTER 2. LOGARITHMS Example 3: Simplify to one log QUESTION Write 2 log 3 + log 2− log 5 as the logarithm of a single num ...

CHAPTER 2. LOGARITHMS 2.11 SOLUTION Step 1 : Taking the log of bothsides log 25x= log 50 Step 2 : Use Law 5 x log 25 = log 50 St ...

2.11 CHAPTER 2. LOGARITHMS Example 5: Exponential Equation QUESTION Solve for x in 7. 5 (3x+3)= 35 SOLUTION Step 1 : Identify th ...

CHAPTER 2. LOGARITHMS 2.12 2.12 Logarithmic Applications in the Real World EMCM Logarithms are part of anumber of formulae used ...

2.12 CHAPTER 2. LOGARITHMS More practice video solutions or help at http://www.everythingmaths.co.za (1.) 01br (2.) 01bs Example ...

CHAPTER 2. LOGARITHMS 2.12 Show that loga �√b x � = loga(x) b Without using a calculator show that: log 75 16 − 2 log 5 9 + ...

2.12 CHAPTER 2. LOGARITHMS More practice video solutions or help at http://www.everythingmaths.co.za (1.) 01bt (2.) 01bu (3.) 01 ...

Sequences and Series 3 3.1 Introduction EMCN In this chapter we extendthe arithmetic and quadratic sequences studied inearlier g ...

3.2 CHAPTER 3. SEQUENCES AND SERIES 5. 3; 0;− 3;− 6;− 9;− 12;... General Equation for the n th -Term of an Arithmetic Sequence E ...

CHAPTER 3. SEQUENCES AND SERIES 3.3 Extension: Plotting a graph of terms in an arithmetic sequence Plotting a graph of theterms ...

3.3 CHAPTER 3. SEQUENCES AND SERIES Example - A Flu Epidemic EMCR Extension: What is influenza? Influenza (commonly called “flu” ...

CHAPTER 3. SEQUENCES AND SERIES 3.3 You sneeze and the virus is carried over to 2 people who start the chain (a 1 = 2). The next ...

3.3 CHAPTER 3. SEQUENCES AND SERIES Or, after how many days would 16 384 people be newly-infected with the flu virus? an = a 1 . ...

CHAPTER 3. SEQUENCES AND SERIES 3.4 3.4 Recursive Formulae for Sequences EMCT When discussing arithmetic and quadratic sequences ...

3.5 CHAPTER 3. SEQUENCES AND SERIES the previous two terms.Hence, we can write down the recursive equation: an= an− 1 +an− 2 (3. ...

CHAPTER 3. SEQUENCES AND SERIES 3.5 m is the lower bound (or start index), shown belowthe summation symbol; n is the upper boun ...

3.6 CHAPTER 3. SEQUENCES AND SERIES Exercise 3 - 2 What is �^4 k=1 2? Determine �^3 i=− 1 i. Expand �^5 k=0 i. Calculate ...

CHAPTER 3. SEQUENCES AND SERIES 3.6 Because all the terms are equal to 1 , it means that if we sumto n we will be adding n-numbe ...