Daily study session 3: Indices and Logarithm

Daily Study Session 3: Indices and Logarithm

Please answer the following questions:

Daily study session 2:

Hi all students, the questions for the daily study session 2 is available now.

Please try out and send me the answer

 

Answer:

Q1

(a)

 2^x=y

2^(x+3) = (2^x) (2^3) = y(2^3) = 8y

(b)

4[(2^3)^(1-x)] = 4[8^(1-x)]

=4[(8^1)/(8^x)]

=4[8((2^3)^x)]

=4[8((2^x)^3)]

=4[8(y^3)]

=32(y^3)

(c)

8[4^(x-2)]

=8[(4^x)/(4^2)]

=8[((2^2)^x)/16]

=8[((2^x)^2)/16]

=8[(y^2)/16]

=(y^2)/2

(d)

(8^x) - (4^-x)

= [(2^3)^x]-[(2^2)^(-x)]

=[(2^x)^3]-[(2^x)^(-2)]

=(y^3)-(y^(-2))

= (y^3)-[1/(y^2)]

Q2

{[8(x^2)]^(8-r)} {[1/(2x)]^r}

={[(2^3)(x^2)]^(8-r)}{[(2x)^(-1)]^r}

={(2^3)^(8-r)}{(x^2)^(8-r)}{2^(-r)}{x^(-r)}

=[2^(24-3r)][ x^(16-2r)][2^(-r)][x^(-r)]

=[2^(24-3r-r)][x^(16-2r-r)]

=[2^(24-4r)][x^(16-3r)] (shown)

Daily Study Session 1: Answer

The answer of the daily study session 1 is available here. You may check your answer here.

疑难解答 （１）：Maths（GEOMETRIC PROGRESSION）

Source from Wikipedia:

Question from Students:

Using the concept and the basic knowledge shown above:

Daily Study Session 1: hint

For Form 3 entering Form 4 students or any students never study about indices topic, you may refer tothe hint here

Indices

Note:

Additinal Maths: Quadratics (SPM/IGCSE)

For IGCSE and SPM students who taking additional Maths, please try out this questions.
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