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Q1)
Evaluate the following Logarithms to 2 decimal places:
a)
log
3
15 =
b)
log
4
15 =
c)
log
5
15 =
d)
log
3
30 =
e)
log
7
26 =
f)
log
9
130 =
g)
log
12
20 =
h)
log
15
3 =
i)
log
6
15 =
j)
log
4
17 =
Q2)
Given that
log
b
2 = 0.481
and that
log
b
3 = 0.762
calculate:
Give answers to 3 decimal places:
a)
log
b
6 =
b)
log
b
4 =
c)
log
b
8 =
d)
log
b
9 =
e)
log
b
18 =
f)
log
b
36 =
g)
log
b
72 =
h)
log
b
64 =
i)
log
b
81 =
j)
log
b
1.5 =
Q3)
Given that
log
b
27 = 1.431
then the value of
log
b
9
is:
log
b
9 =
Q4)
Given that
log
10
7 = a
then the value of
log
10
(1/70)
is:
Q5)
Express
2 log
4
4x + (1/2) log
4
36 x
6
–
2
in the form
log
4
(a x
b
)
log
x
4
Q6)
Express
3 log
5
3x
4
+ (1/3) log
5
64 x
9
–
2
in the form
log
5
(a x
b
)
log
x
5
Q7)
Express
(1/2) log
7
81x
8
–
2 log
7
3 x
9
+ 3
in the form
log
7
(a x
b
)
log
x
7
Q8)
Express
3 log
3
3x
3
–
2 log
3
18 x
2
+ 4
in the form
log
7
(a x
b
)
log
x
3
Q9)
Solve the following equation:
x + 2
x
–
4
4
=
3
x =
Q10)
Solve the following equation:
x + 4
x
–
1
2
=
5
x =
Q11)
Solve the following equation:
x + 9
x
–
4
3
=
7
x =
Q12)
The value of an investment fund is given by the equation
V = 4600 (1.045)
n
where
n
is the number of years after the initial investment.
a) What is the value of the initial investment?
b) How long until the investment is worth £7,000?
c) How long until the investment doubles in value?
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