1970-03-03 — Page 22

郭日僑華

二期星日三月三年〇七九一圈公年九十五國民華中 育教僑華

買-第張六第日六廿月正年戌庚藤夏 WAH KiU YAT PO

&#8#3#$%$#$%$#S+

Example

prova. if a +

then log

新橋

#$%

(10ga +logb)

Since a

2ab

b)2

9ab

10英文中學會考試題預習專欄

堅道英文書院主編

英文科

英文中學會考試題預習專欄

b)2 = log (Jab)

2log (a + b) = 10g a + log b + log 9

log(atb) = 2(log a + log b) + ✯ 108 9

(十八)

ENGLISH LANGUAGE (18)

log(e±b). - 10g:3 - *(log a + log b)

Answera to Exercise 17

19. (A)

* 堅道英文書院主編 數學科

(108

fog a + log b).

2. (B)

20, (B)

3. (0)

21. (D)

(十八)

Indical Equations Any equation involving the variabla (or variables) in the indices of the numbers. present is known as an indicial equation.

4. (A)

22. (0)

5. (A)

23. (0)

6. (B)

24. (B)

MATHEMATICS" (18)

There are two " main typse of indicial equations to be considered as follower

7. (0)

25. (B)

26.

9.

Logarithas

Definition If y» a"

10.

11.

logarithm of cho tha This can be

han ris, naid to be the

then x = log:

involving x.

12. (B)

13. (B)

14. (B)

32.

15. (B)

33.

16. (0)

34.

17. (B)

35.

18. (B)

27. (D) 28. (D) 29(D)

30. 32. (D)

1084 16

Then the Yuso je 10, the logarithes are known as common legarithme, and when the base is o (2.71828

*.), the logarithms are known as Natural or Napierian Logaritham,

The following are the main properties of logarithms (1) If 'a? Am a mon-negative number such that a 41, then a” is always positive, for all values of x (x may be -va, 0 or +ve). Henos, it is meaninglong tɩ say log of a -ve number or log, of ZORO.

(2) 108 1 0 for any non-SOTO

(3) log a × 1 for any non-zero

(4) 108 (MN) ➡ 10g X + 10g ▼

(5) 105, ( *) × 108 X = log ▼ (6) 108 ̧(N*)

(+ve, (7) 1988 Noter (1)

(2) 106.

(3) 108 N

klog N, for any values of 'k'

fraction or integer)

(1) the straightforward oases which can be solved

by taking logarithms to the base 10, (ii) those which can be reduced to a quadratic in y,

where ya and f(x) means any expression

Note: No base is shown in the case of common

logarithms.

Example 4 Solve 63x + 1 315x - 2 21

Taking logarithms to the base 10 for the equation

(3x + 1)log 6 + (15% −2) log 3 = log 21

(3 1og 6 + 15 log 3)x - log21

21 – log 6 + 2 log 3

3 log 6 + 15 log 3

1.3222 – 0.7782 + 0.9542

3 x 0.7762 + 15 x 0.4971

0.16 (corr. to 2 deo.)

Example 5 Solve the equation

25 82

logó + 210g.

Taking logarithms to the base 10 for the equation

1082 + 10g5 10882x+1

xlog2 + (1 −1)log5 - (2x + 1) log 8

xlog2 + xlog 5 - 2x log 8 = 10g 8 + log 5

[1032 + 1085 – 2 log 8] = 10g

(2 x 5)

x108

= log(8 x 57

108 108 N

(4) From property (5) above, when X -

(5) Logarithm to base 10 is called common

logarithm.

Example 1 Simplify (a) 210g - 1937 + 21083 + $10849

(b) (log2)3 + (log5)3+(log5)(logs).

(a) Exp. - (logy)2 1087 +1083 10849

82. 108 40

10832

10g 40

(10g 5-10g 32)

1.6021

0.6990 – 1.5051

-1.987

Solution

(b) Exp.

108 1

→ – – 108 N

108 ( 3 x 4 x 9 x 1

Ceaple 6

15

and deduce

Using the given data in

27

(2) 12

(5)/(4)

+108:5

Batisfied by the valios

• 8, y - 27, show the values of sand

log 100.

(log2)3 + (1685)3 + (1085)(10823) (1082 + 10g5) [(10g2)2=(log2)(10g5}

(Log5)2]+ 3(log5)(log2)

- [108(215)] [(10g2)2 - (log2)(1085)

(1085)2] + 3(log5)(log2) (10g2)2 + 2(1082)(log5) + (log5)♬

(10g 2 + log 5)* (108:10)2

Example 2 Solve the equations.

(i) log (5x − 6) + Log (2x + 3) = log (10x2 - 31)- 5)

(ii) 2 10g (x − 2) = 10g (2x - 5)

(±) 108 (5x − 6) + 10g (2x + 3) × 10g (10x=.

Taking logarithms to the base 10

10g 2.4 log. 2

Using aqt, (b) £m nqb (4)

1.483

Solution

10g (5x − 6)(2x + 3) = log ̧ (10x2

(5x - 6)(2x + 3) - 10x -

10x2

+3x-18 = 10x

6x13 1.0.

(ii) 210g (x − 2) - log (2x

log (x − 2)2

≈ 108, (2x

[(1)

..(2)

..(3)

.2 (2-1) ...(4)

2M (2n-1) **(5)

2.4

(6)

Using e (6)

6,429

(1) and this value for b

(b) 32

Solution

the eqt becom

be real than

Taking logarithas to the bass 10

108

2 log 7

2.807

Exercise 18

Precis

Read the following passage carefullyt

We generally speak of our senses as being five sight, hearing, taste, smell and touch. But these five are really forms of one, namely feeling. By touch we can feel the shape, sise, roughness of smoothness, dryness or dampassa, of objects. The specialised nerve endings in the tongue and palate' enable us to feel another quality of things, which simple touch does not; and this is closely connected. with the peculiar power of the nose to feel the minute partioles in the air which give rise to amell, The ear pan fost certain waves in the air which the brain translaw into sound; and the sys 18 A marvellous mechanism for feeling the ether waves, which the braia interprets as light. It is possible, that some aninals have other senses of which we know nothing, for they sometimes beem to become aware of things of which one of our senses give us any informations and people, somatinas upeak of such power as a "sixth sense.

Our senses are our only means or communicating with the world around my

pro

thêm all, he would be completely cut off from the world, like a captive in an underground dungeon. There was a case almost as bad as this sone jgara, ago, which caused a gragt stir in Anazion. Helen Keller was bora blind, deaf and dumb. The only sense she had really, was touch; for, ever taste and omell were but poorly developed. The story of how her nurse,

a highly educated lady, eventually, after years of trying," got inte touch with the poor little imprisoned soul simply through the sense of touch, is a wonderful romance, To-day Helen Keller, who

cannot ass, nor hear, nor speak, has become herseir an educated lady, has taken a university degree and written a book.

This is an extreme oase, But the less or one or two of the senses is not an uncommon affliction. The loss of the sense of smell or of taste, although unpleasant,

t, ie not a serious drawback to life; but loss of hearing, or sight, or both, is indeed a calamity.

of the two, deafness, or loss or nearing, 18 the lesser evil bad enough as it is. A deaf man cannot receive any. communications from his fellows exoept by signs (the deaf and dumb alphabet), or by writing. He is deprived of all the joys of musie, and lives in a world of total silence. He therefers loses much of the joy of life. Still, if he retains his sight, he can get along. Beethoven, one of the greatest of the world's musicians, was totally donf.

But blindness is a much more serious deprivation. To dwell in total darkness, never to see the sunlight, the flowers, the faces of friends and loved ones, to be unable to read booka, - what a terrible life! And, yet the blind are generally people of a very happy? disposition; and in time they manage to overcome aone of the disabilities of blindness. Their other donses seem to develop wonderful sensitiveness to compensate for the loss of sight. Their touch is more delicate, the sense of smell very keen, and their hearing becomes so acute that they can hear. sounds and shades of sounds that a seeing man cannot. The invention of the Braille System of raised letters enables then to read with their fingera; and they. learn to be very skilful in making things with their.

hands. We rightly pity the blinds and yet they do not seem to pity themselves, Men of genius, like the Greek post Homer, and the English poet Milton, have rison above their blindness; and the career of Henry Fawcett, "who after he had lost his sight became Post-Master General and a noted political economist, provas how wonderfully a man may overcome this sad dionöfli

13 Kake a summary of the above passage in

not more than 200 words.

(未完轉入第六張第三頁)

{y - 1)(y − 2)

~(1) (a)

42

3-(twice)

replacing

(3x)2 therefore

From

Zoon (2) saking logarithas to the bass

* 1bg 3.- Log 2.

66309