SCHOOL OF SCIENCE AND TECHNOLOGY, SINGAPORE
MATHEMATICS DEPARTMENT 2022
SECONDARY 3 ADDITIONAL MATHEMATICS
LOGARITHM HOMEWORK 2
Name: ____________________________ (
)
Class: _____________
Ex5.3Q3
Without using a calculator, evaluate each of the following.
b)
a)
log2 32 =
c)
log4 0.125 =
d)
Date: _______________
log27 3 =
log1 8 =
2
Ex5.3Q4
a)
Can a logarithm be a negative value? Justify b)
your answer.
Can we take the logarithm of a negative number?
Explain.
Ex5.3Q6 (Convert each of the following to log form)
c)
4𝑥 = 2 − 𝑘
d)
𝑒𝑥+5 = 𝑚 − 2
Ex5.3Q7 (Convert each of the following to index form)
c)
lg(𝑥 − 𝑦) = 2
d)
log2 (4𝑦) = 𝑝 + 1
Ex5.3Q8 (Express y in terms of x)
b)
2 lg 𝑦 = 𝑥 − 2
c)
𝑒2𝑦 + 4 = 𝑥
Ex5.3Q9b
Ex5.3Q10a
Find the range of values of x for which log𝑥 (𝑥 − 3) is Given that log4 𝑥 = 2 and log2 𝑦 = 3, evaluate 𝑥.
𝑦
defined.
Ex5.3Q10b
Ex5.3Q11
2
Given that log𝑥 𝑎 = 1 and log𝑦 𝑏 = 2, express 𝑥𝑦 in Without using a calculator, evaluate each of the
following.
terms of a and b.
a) (3 − log3 3)3 =
Ex5.3Q12
8
c) log𝑎 50 + log𝑎 25
+ 2 log𝑎 10 − log𝑎 25
3 log 𝑥+2 2
b)
𝑥
( 4−2 log5 1 ) =
c)
log2 (4 − 2 lg 10) =
d)
1
log𝑎 2 + log𝑎 √18
2
Ex5.3Q13
Show that
a)
2 log𝑎 2 + log𝑎 10 − 3 log𝑎 3 − log𝑎 5 = 3 log𝑎 23
DSS2015
Given that 𝑥 = 3𝑘 , express
log𝑥 9 + log√3 𝑥
terms of k.
b)
log2 27 × log3 25 × log5 16 = 24
FMS2015
Given that
log𝑥 𝑦 + log𝑦 𝑥 −
express y in terms of x.
5
= 0,
log𝑥 𝑦
CHIJTPY2013
Given that 𝑥 = log2 𝑎 and 𝑦 = log2 𝑏, express
log𝑎 √𝑎𝑏3
in terms of x and y.
DSS2013
Find 𝑥 in terms of a and b for the equation
(log𝑎 𝑥)log𝑏 𝑥 = 𝑥,
where a and b are positive real numbers and 𝑎 ≠ 1, 𝑏 ≠
1, 𝑥 ≠ 1.
Ex5.3Q14b
Ex5.3Q15
𝑝
𝑐
Given that log3 𝑝 = 𝑎, log27 𝑞 = 𝑏 and 𝑞 = 3 , express Given that 𝑦 = √20 × 10−3𝑥 × 105𝑥 and
√5
c in terms of a and b.
lg 𝑦 − 𝑚𝑥 = 𝑐 for 𝑥 > 0 and 𝑦 > 0,
find the value of m and of c.