Lesson Summary (February 27, 2013)

Worksheet A02d
6) log₅(log₃x)=log₁₀₀100
log₅(log₃x)=1
log₃x=5¹
x=3⁵
  =243

7) log₅x=a            log√5y=b
express xy² as a power of 5
x=5ª                      y=√5ᵇ
                               =5^b/2

xy²=5ª x 5^2b/2
     =5^a+2b/2
     =5^a+b

*Don't cancel your answer even if it seems wrong (sometimes it might be correct) only cancel after realising the mistake and redoing.

Worksheet A02e
9) 6ⁿ + 6^n+1 + 6^+2
= 6ⁿ+6ⁿ6+6ⁿ6²
= 6ⁿ(1+6+36)
= 6ⁿ(43)
∴divisible by 43 for all natural values of n.

11) log₅(5-4x) = log√5(2-x)
                        = log₅(2-x)/log₅5^1/2
                        = log₅(2-x)/(1/2)
                        = log₅(2-x)²

5-4x = (2-x)²
        = 4 - 4x + x²
x²=1
x=±1

* Sorry for the late post

Lesson Summary (February 26th 2013)

Morning Lesson:

We learnt how to solve logarithms using different methods.

Method 1: Covert log form to exponential form.
Method 2: Use change of base formula first.

For example:

Afternoon Lesson:

From the tables we have calculated out, we can conclude that:

- Power:   log_a (x^p) = p log_a x

-  Product: log_a (xy) = log_a x + log_a y

- Quotient:  

A formula can also be inputed into your graphic calculator to help change base:

Sorry I will input the formula when I get the paper back ><

Otherwise, you can use this log rule to change base too:

- Change of base formula: 

http://www.mathwords.com/c/change_of_base_formula.htm

Things to take note:

log_a (x + y) ≠ log_a x + log_a y

log_a (x – y) ≠ log_a x – log_a y

Applications OF Exponential and Logarithm

APPLICATIONS:

OF EXPONENTIAL

GRAPHING EXPONENTIAL

====================================================

OF LOGARITHM

GRAPHING LOGARITHMS

 ====================================================

KEY RULES OF LOGARITHMS

 ====================================================

GUIDELINES TO SOLVE LOGARITHMS

TI84plus : Logarithms - Change of Base

TI84plus : Logarithms - Change of Base

How to use TI84 to Calculate Log of a different Base

How to Programme Change of Base

TI84 Solving Quadratic

Solving Quadratic Equation Using TI8plus programme

Lesson Summary 19/2/2013: Wee Chang Han

Logarithm 

Laws of Logarithm:

1.

a^x = y

is equals to:

log a(y) = x

2. 

log10 = lg

log e = l(n), n = natural log.

3.

lg 1 = 0

log10 (1) = 0

10^0 = 1

Because:

loga(1) = 0

a ^0 = 1

where a ≠0.

4.

loga(a) = 1

where a ≠ 0, a >0

log10(10) = 1

because:

log10(10) = 1

10^1 = 10

Note:

5.

log10(-5) = error?

why?

-5 = 10^?

there is no value for the power of 10 to become -5, therefore log a base b = c, where a ≠ a negative integer or  < 0.

6.

loga(b) = log10(b) / log10(a)

            = ln(b) / ln(a)

            

caution!:

lg(b)/lg(a) ≠ b/a (do not cancel!!)

Correct:

lg(b)/ lg(a) = calculate both the top and the bottom.

7.

logc(ab) = logc(a) + logc(b)

8.

logc (a/b) = logc (a) - logc (b)

9.

log10(100) = log10(10)^2

                  = 2log10(10)

                  = 2

note:

loga(b)^n = n loga(b)

Using TI 84Plus and simple programme

INTRODUCTION TO TI84 Plus

Programming QUADRATIC INTO TI84 

Study the video provided for clarity of concept and greater appreciation of TI84plus.

Task 1: Simulate the programme into your TI84plus. Call it QUAD

Task 2: Extend your learning by considering the case when the answers are not Real ie. Imaginary