134 Logarithms (Chapter 5)
EXERCISE 5B
1 Write an equivalent exponential equation for:
a log 10 100 = 2 b log 10 10 000 = 4 c log 10 (0:1) =¡ 1
d log 10
p
10 =^12 e log 2 8=3 f log 3 9=2
g log 2 (^14 )=¡ 2 h log 3
p
27 = 1: 5 i log 5
³
p^1
5
́
=¡^12
2 Write an equivalent logarithmic equation for:
a 22 =4 b 43 =64 c 52 =25
d 72 =49 e 26 =64 f 2 ¡^3 =^18
g 10 ¡^2 =0: 01 h 2 ¡^1 =^12 i 3 ¡^3 = 271
Example 6 Self Tutor
Find:
a log 216 b log 50 : 2 c log 105
p
100 d log 2
³
p^1
2
́
a log 216
= log 224
=4
b log 50 : 2
= log 5 (^15 )
= log 55 ¡^1
=¡ 1
c log 105
p
100
= log 10
¡
102
¢^15
= log 1010
2
5
=^25
d log 2
³
p^1
2
́
= log 22
¡^12
=¡^12
3 Find:
a log 10 100 000 b log 10 (0:01) c log 3
p
3 d log 28
e log 264 f log 2128 g log 525 h log 5125
i log 2 (0:125) j log 93 k log 416 l log 366
m log 3243 n log 23
p
2 o logaan p log 82
q logt
³
1
t
́
r log 66
p
6 s log 41 t log 99
4 Use your calculator to find:
a log 10152 b log 1025 c log 1074 d log 100 : 8
5 Solve forx:
a log 2 x=3 b log 4 x=^12 c logx81 = 4 d log 2 (x¡6) = 3
6 Simplify:
a log 416 b log 24 c log 3
¡ 1
3
¢
d log 104
p
1000
e log 7
³
p^1
7
́
f log 5 (25
p
5) g log 3
³
p^1
27
́
h log 4
³
1
2
p
2
́
i logxx^2 j logx
p
x k logmm^3 l logx(x
p
x)
m logn
³
1
n
́
n loga
³
1
a^2
́
o loga
μ
1
p
a
¶
p logm
p
m^5
cyan magenta yellow black
(^05255075950525507595)
100 100
(^05255075950525507595)
100 100 4037 Cambridge
Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_05\134CamAdd_05.cdr Tuesday, 21 January 2014 2:47:31 PM BRIAN