Topic 5-Indices Surds Logarithms
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Transcript of Topic 5-Indices Surds Logarithms
by Mr Teh DEC 2010
topic 5:Indices Surds Logarithms “A stupid question is the one not asked”
E: [email protected] ~ 1 ~ If you find this useful, CALL
+65-9832 2013 and ask for MORE
Question 1:
Solve, for x and y, the simultaneous equations.
27193
428
2 =÷
=
+xy
y
x
Question 2:
Evaluate 212
2
273)3(819++ ×
×xx
xx.
Question 3:
Solve )5(54 3323
++÷= xxx
.
Question 4:
Given that cba xxx 32)216()36( 32
323
4 =÷−− , find the values of a, b and
c.
Question 5:
Show that if n is a positive integer, 3221 3)3(6)9(7 ++ +− nnn is exactly
divisible by 14.
Question 6:
Given that baxxx )3(27814
41
343
37
23
=
÷
, find the value of a and of
b.
Question 7:
The equation 8)2(23)2(722 −=− ++ ababa has a solution 1=a .
(a) Find the value of b (b) Hence, find the other solution of a.
Question 8:
Solve 17 42
=−x .
by Mr Teh DEC 2010
topic 5:Indices Surds Logarithms “A stupid question is the one not asked”
E: [email protected] ~ 2 ~ If you find this useful, CALL
+65-9832 2013 and ask for MORE
Question 9:
Solve 84)3(93 1 =+− xx .
Question 10:
Solve 342 21 =+ −+ xx .
Question 11:
A cuboid has a square base of side ( )cm 57 − . The volume of the
cuboid is ( ) 3cm 776590 − . Find the height of the cuboid,
expressing your answer in the form ( )cm 75 ba + , where a and b
are constants.
Question 12:
The diagram shows a cylinder with a base area of ( ) 2m 852 − .
Given that the volume of the cylinder is ( ) 3m 5287 − , find the
height of the cylinder in the form ( )m 10qp + where p and q are
integers.
Question 13:
Solve 1103 −= xx .
Question 14:
A rectangle has a length of ( )m 22 − and an area of ( ) 2m 232 + .
Find the breadth of the rectangle in the form ( )m 2ba + , where a and b are integers.
Cross sectional area
= ( ) 2m 852 −
height
by Mr Teh DEC 2010
topic 5:Indices Surds Logarithms “A stupid question is the one not asked”
E: [email protected] ~ 3 ~ If you find this useful, CALL
+65-9832 2013 and ask for MORE
Question 15:
Express 347
1−
in the form 3ba + .
Question 16:
Given that m = 2x and n = 2y, express
16
log2
2nm
in terms of x and y.
Question 17:
Given that mx =5log and ny =5log , express the following in terms
of m and n.
(a) xy
(b)
25
25log
yx
Question 18:
Given that xm 3= and yn 3= , express the following in terms of x and y.
(a) mn27log3
(b) nm 819 loglog +
Question 19:
Given that log7 x = p and log7 y = q, express the following in terms of p and q
(i) 3
2
749log
yx
(ii) xy
Question 20:
Solve ( ) ( ) 2log4212log23log 555 −=−−+ xx .
Question 21:
Solve the equation 26)(710 2 += xx ee .
by Mr Teh DEC 2010
topic 5:Indices Surds Logarithms “A stupid question is the one not asked”
E: [email protected] ~ 4 ~ If you find this useful, CALL
+65-9832 2013 and ask for MORE
Question 22:
Solve 0763 =+− xx
ee .
Question 23:
Solve 03)2(134 1 =+−+ xx .
Question 24:
Solve the simultaneous equations.
2lg33lg)36lg(5255 1
+=+×=+
yx
yx
Question 25:
Solve 2523 x−= , giving your answer correct to 2 decimal places where
necessary.
Question 26:
Solve 3log1)1(log1log 2739 +=−+− xx .
Question 27:
Solve 2)4(loglog 42 −=+ xx .
Question 28:
Solve 116loglog4 =− xx .
Question 29:
Solve 35log2log5 =+ xx .
Question 30:
Evaluate the value of p, without using a calculator. 23log8log3 =− pp