TOPIC 16 | logarithm change of base set 1 of 10 get the full set details at the bottom of page
Question 1:
8
Solve log2 x + log8 x =
3
Question 2:
Simplify log8 32 − log16 8 − log32 4 − log64 2 without using calculator
Question 3:
Given that log
=
log2
2a
1
− log4 c , express a in terms of b and c
b
Question 4:
Without the use of a calculator, show that
(log2 10)(log 5 4)
=8
log25 10
Question 5:
If log k a = x and log k b = y , express each of the following in terms of x and
y
(i) log ab k
(ii) logb ab 2 k
Question 6:
Solve 5 lg x + 2 =
3logx 10
Question 7:
Given that log2 p = x , express log p 4p in terms of x
Question 8:
(a) Given that x = log2 a is a solution of the equation 4 x − 2x+2 =
21 , find the
value of a.
(b) If log4 a = m , without using a calculator, express
a
in terms of m
64
(ii) 2m−1 in terms of a
(iii) log16 16a in terms of m
(i) log4
Page
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TOPIC 16 | logarithm change of base set 1 of 10 get the full set details at the bottom of page
Question 9:
Solve log3 x − 4 logx 3 =
log6 1
Question 10:
Given that log3 x = k express logx 3 + log9 x in terms of k
2
2logx 2
Solve log2 x + 3 =
Question 11:
Given that q = log4 p , express, in terms of q
1
(i) log4  
p
(ii) log2 4p
Question 12:
3
, express each of the following in terms of a
Given that log 5 6 × log36 125 =
2
and b
1
(i) logx 12
2
(ii) lg x
Question 13:
Evaluate log a a 2
Question 14:
Evaluate log3 5 × log 5 27
Question 15:
Solve In x 2 − 3logx e =
1
Question 16:
Solve log 3 y + log y 3 =
2
Question 17:
Solve log2 x = 2logx 2
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TOPIC 16 | logarithm change of base set 1 of 10 get the full set details at the bottom of page
Question 18:
Evaluate log4 p × log p 16 + log p p
Question 19:
Solve log3 x 2 = logx 81
Question 20:
Evaluate logx 27 × log9 x
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