G11HL-Logs &;Exp
4a. Show that
where
10 g
=
ㆍ융
vR
1 ogpx =
AFL
황0
gr
.
gv 김
4b. It is given that
. Express in terms of . Give your answer in the form
, where p , q are constants.
i
1 ogzytlogz 기 + 10gz (2x )
=0
1
logz y )=( 21
R o
1
도
ㅅ
2
Y설
=
갈가
_____________(2,5)
= 열기에
I = Y( (27
6. Find the solution of
l0
같= g
gz
0
.
리z
D= 60
60
_____________(4)
24. Solve the equation
기
22 = 2기 t 8
.
t트 4 t 32 = 0
-
π 220 -2 가
'
기
2
=
=
-
ct + 4) ( t 8 =O
0
-
it
-
10. Find integer values of
m=
1
tEX4
-
즈t
t
=
등
and
o아
8
2
8
=
3
_____________(5)
구
=
for which
og3 (29 X35X2 )
n
니z 5
기
=
5 l 10 g36
MF5
-
m =5
n=
5
-
_____________(4)
16. Consider
. Given that
, find the value of a.
~
log
10
a=
2
31
gog ㆍ
g 4
32 = 5
.
2
X
g
X
…
X
ilog
π
10g
3z
g3
=
름
름
g
=
2
1
비oY
g:
내
5
_____________(5)
11a. It has been suggested that in rowing competitions the time,
seconds taken to complete a 2000 m
race can be modelled by an equation of the form
is the number of rowers in the boat
ㅡ
, where
and and are constants for rowers of a similar standard.
To test this model the times for the finalists in all the 2000 m men’s races at a recent Olympic games
~
were recorded and the mean calculated.
The results are shown in the following table for
and
.
Use these results to find estimates for the value of and the value of .
Give your answers to five significant figures.
b=
-
0 105673
a = 420 b5
-
420 .65 ÷
b=
d
2
oaza 37키 =
=
3a 094 = azb
olo5 ba
_____________(4)
logz oa 29구 7키
-
11b. Use this model to estimate the mean time for the finalists in an Olympic race for boats with 8 rowers.
ㅡ
Give your answer correct to two decimal places.
420 65 X 8
-
0 60507
337 6 b7
.
=
3767
.
.
_____________(1)
11c. It is now given that the mean time in the final for boats with 8 rowers was 342.08 seconds.
Calculate the error in your estimate as a percentage of the actual value.
XN 0 = 12891
34200 - 337이크
129 %
_____________(1)
3420 b
11d. Comment on the likely validity of the model as
likely
Mof to be
likely
fo be &uite
a
good fit for larger
2
게
(loseto
. Express your answer in terms of
and
231
=
=
X
33
_____________(2)
.
3
=
3기
310 g32 = 3기
JM 2
10 g32 = 럴
=
-
IM2
IM 3
_____________(5)
231
) X33
-
og 3 2
-
헉
ㅡ
가
기
-
-
of N
~
231
/ 23
1
Values
good fif for Values
a
17. Solve the equation
(3가-
increases beyond 8.
채
3
2
18a. The diagram below shows a sketch of the graph of
. Sketch the graph of
on the same
J
axes.
18b. State the range of
.
D
CI ∞ )
…
18c. Given that
, find the
value of and the value of .
atb= O
Iu (Katb =o
4at 며
a=
국 여취
_____________(2,1,4)
19. Solve the following equations:
(a)
(P
;
1
1 ogz (가-2 )
= l0 gz기르기시 ) Ʃ
2) 2 =7(즈6+ 12
-
=
2어 8
=4
def- Of1 og usetve
(b)
(
ogexIn 기 oge
u기
1oge 7(
3
( Iux)
=
3
( Iux ) = (Inn( )
ecIux)
z
=
패가 XJ 패기 =
(Iu기73
(n기 P ( Zul - 1
패기 =
가
>
r
.
4
O
기르4기+ =가르크기시 2
=
이아
= 0
2= ore
그
_____________(8)
ore
그
20. The first terms of an arithmetic sequence are
ㅡ
Find x if the sum of the first 20 terms of the sequence is equal to 100.
m
…
a=
ogz
[
C=
2
…
log21
logzx
''
에
많을 꽃해
행에
+
러
=
4
기 = 16
4.
시야
3
-
109 m
.= .
16
_____________(6)
22. Let
. The graph of f is transformed into the graph of the function g by a translation of
, followed by a reflection in the x-axis. Find an expression for
, giving your answer as a single
logarithm.
yt2 =Iu( -33 Y 패- 가- - )
가
(
2
3
=
-Iu(n 3) + Inez
~
패
=
25. (a)
Find the solution of the equation
패
-
더
4 ( 1 c1 = In 24
expressing your answer in terms of
.
패 24
=
=
(b)
3c+ 51
f
IM 2
+ 15
In 2371
Using this value of x, find the value of a for which
231+ ( 5
x-
-
=
개
웩
_____________(5)
+
1
-
410g 22
2가
4 ( 1 2기 )
-
1
-Iu
C1- 16 )In 2
C
K+ 1 b퍼 2
x= ~
8 + In그
, giving your answer to three decimal
~
places.
a= x
a=
1 318
1 318
_____________(6)
.
.
26. Let
. Find the product of the zeros of g .
=
10 g512 log37 x = o
1210gmF #
10g3
뀔
210 g 기 =± 1
가
약
3
X
4a. Show that
iil 210
i ) 210g3 기며
=
where
g3
=- 1
log3 = 는
기
=
그
_____________(5)
.
_____________(2)
X
4b. It is given that
.
Express in terms of . Give your answer in the form
, where p , q are constants.
_____________(5)
4