SELINA Solutions for Class 9 Maths Chapter 8 - Logarithms

Enjoy access to 24x7 free Selina Solutions for ICSE Class 9 Mathematics Chapter 8 Logarithms at TopperLearning. Now, quickly revise the steps to express the given terms in log 2 and log 3 form with our online textbook solutions. Also, practise using the various laws of logarithm for computing the solutions for textbook problems.

In the Selina textbook solutions, you can also practise the ICSE Class 9 Maths True or False questions based on logarithms. For help with the tricky questions from this chapter, look for answers in our portal’s doubts and solutions section.

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Chapter 8 - Logarithms Exercise Ex. 8(B)

Question 1

Express in terms of log 2 and log 3:

(i) log 36 (ii) log 144 (iii) log 4.5

(iv) log - log (v) log log + log

Solution 1

(i)

(ii)

(iii)

(iv)

(v)

Question 2

Express each of the following in a form free from logarithm:

(i) 2 log x - log y = 1

(ii) 2 log x + 3 log y = log a

(iii) a log x - b log y = 2 log 3

Solution 2

(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

(iii) 

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

Question 3

Evaluate each of the following without using tables:

(i) log 5 + log 8 - 2 log 2

(ii) log108 + log1025 + 2 log103 - log1018

(iii) log 4 + Selina Solutions Icse Class 9 Mathematics Chapter - Logarithmslog 125 - Selina Solutions Icse Class 9 Mathematics Chapter - Logarithmslog 32

 

Solution 3

(i) Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms 

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

(ii) Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms 

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

 

 

(iii) Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms 

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

Question 4

Prove that:

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

Solution 4

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

 

Question 5

Find x, if:

x - log 48 + 3 log 2 = Selina Solutions Icse Class 9 Mathematics Chapter - Logarithmslog 125 - log 3.

 

Solution 5

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

 

 

Question 6

Express log102 + 1 in the form of log10x.

Solution 6

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

Question 7

Solve for x:

(i) log10 (x - 10) = 1

(ii) log (x2 - 21) = 2

(iii) log (x - 2) + log (x + 2) = log 5

(iv) log (x + 5) + log (x - 5)

= 4 log 2 + 2 log 3

Solution 7

(i) 

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

(iii)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

(iv)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

Question 8

Solve for x:

(i) Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

(ii) Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

(iii) Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

(iv) Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

Solution 8

(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

 

(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

 

(iii)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

 

(iv)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

Question 9

Given log x = m + n and log y = m - n, express the value oflog Selina Solutions Icse Class 9 Mathematics Chapter - Logarithmsin terms of m and n.

 

Solution 9

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

 

 

 

Question 10

State, true or false:

(i) log 1 Selina Solutions Icse Class 9 Mathematics Chapter - Logarithmslog 1000 = 0

(ii) Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

(iii) If Selina Solutions Icse Class 9 Mathematics Chapter - Logarithmsthen x = 2

 

 

(iv) log x Selina Solutions Icse Class 9 Mathematics Chapter - Logarithmslog y = log x + log y

 

Solution 10

(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

 

(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

(iii)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

(iv)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

Question 11

If log102 = a and log103 = b; express each of the following in terms of 'a' and 'b':

(i) log 12(ii) log 2.25(iii) log Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

(iv) log 5.4(v) log 60(iv) log Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

Solution 11

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

(iii)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

 

(iv)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

(v)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

 

(vi)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

Question 12

If log 2 = 0.3010 and log 3 = 0.4771; find the value of:

(i) log 12(ii) log 1.2(iii) log 3.6

(iv) log 15(v) log 25(vi) Selina Solutions Icse Class 9 Mathematics Chapter - Logarithmslog 8

 

Solution 12

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

 

(iii)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

 

(iv)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

(v)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

(vi)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

 

Question 13

Given 2 log10 x + 1 = log10 250, find :

(i) x(ii) log10 2x

Solution 13

(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

 

(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

Question 14

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

Solution 14

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms 

Question 15

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

Solution 15

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms 

Question 16

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

Solution 16

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms 

Chapter 8 - Logarithms Exercise Ex. 8(C)

Question 1

If log10 8 = 0.90; find the value of:

(i) log10 4(ii) log Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

(iii) log 0.125

Solution 1

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

(iii)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

Question 2

If log 27 = 1.431, find the value of :

(i) log 9(ii) log 300

Solution 2

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

Question 3

If log10 a = b, find 103b - 2 in terms of a.

Solution 3

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

Question 4

If log5 x = y, find 52y+ 3 in terms of x.

Solution 4

Question 5

Given: log3 m = x and log3 n = y.

(i) Express 32x - 3 in terms of m.

(ii) Write down 31 - 2y + 3x in terms of m and n.

(iii) If 2 log3 A = 5x - 3y; find A in terms of m and n.

 

Solution 5

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms 

(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

 

(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

 

(iii)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

Question 6

Simplify:

(i) log (a)3 - log a

(ii) log (a)3 Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms log a

Solution 6

(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

Question 7

If log (a + b) = log a + log b, find a in terms of b.

Solution 7

Question 8

Prove that:

(i) (log a)2 - (log b)2 = log Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms. Log (ab)

(ii) If a log b + b log a - 1 = 0, then ba. ab = 10

 

Solution 8

(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

Question 9

(i) If log (a + 1) = log (4a - 3) - log 3; find a.

(ii) If 2 log y - log x - 3 = 0, express x in terms of y.

(iii) Prove that: log10 125 = 3(1 - log102).

 

Solution 9

(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

 

(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

 

(iii)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

Question 10

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

Solution 10

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

Question 11

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

Solution 11

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms 

Chapter 8 - Logarithms Exercise Ex. 8(D)

Question 1

If Selina Solutions Icse Class 9 Mathematics Chapter - Logarithmslog a + Selina Solutions Icse Class 9 Mathematics Chapter - Logarithmslog b - 1 = 0, find the value of a9.b4.

 

Solution 1

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

Question 2

If x = 1 + log 2 - log 5, y = 2 log3 and z = log a - log 5; find the value of a if x + y = 2z.

 

Solution 2

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

 

 

 

 

 

 

Question 3

If x = log 0.6; y = log 1.25 and z = log 3 - 2 log 2, find the values of:

(i) x+y- z        (ii) 5x + y - z

Solution 3

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

Question 4

If a2 = log x, b3 = log y and 3a2 - 2b3 = 6 log z, express y in terms of x and z.

Solution 4

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

Question 5

If log Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms(log a + log b), show that: a2 + b2 = 6ab.

Solution 5

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

Question 6

If a2 + b2 = 23ab, show that:

log Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms(log a + log b).

 

Solution 6

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

Question 7

If m = log 20 and n = log 25, find the value of x, so that: 2 log (x - 4) = 2 m - n.

Solution 7

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

Question 8

Solve for x and y ; if x > 0 and y > 0;log xy = log Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms+ 2 log 2 = 2.

Solution 8

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

Question 9

Find x, if:

(i) logx 625 = -4 

(ii) logx (5x - 6) = 2

 

Solution 9

(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 (ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

Question 10

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms 

Solution 10

 

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms  

 

Question 11

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

Solution 11

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

 

Question 12

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms 

 

Solution 12

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

 

Question 13

Given log10x = 2a and log10y = Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms.

 

 

(i) Write 10a in terms of x.

 

 

(ii) Write 102b + 1 in terms of y.

 

 

(iii) If Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms, express P in terms of x and y.

 

Solution 13

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms


 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Question 14

Solve:

log5(x + 1) - 1 = 1 + log5(x - 1).

Solution 14

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

 

 

Question 15

Solve for x, if:

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms 

 

Solution 15

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

 

Question 16

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms 

Solution 16

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms 

Question 17

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms 

Solution 17

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms 

Question 18

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms 

Solution 18

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms 

Question 19

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms 

Solution 19

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms 

Question 20

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms 

Solution 20

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms 

Question 21

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

Solution 21

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

Question 22

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

Solution 22

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

Chapter 8 - Logarithms Exercise Ex. 8(A)

Question 1

Express each of the following in logarithmic form:

(i) 53 = 125

(ii) 3-2 = Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

(iii) 10-3 = 0.001

 

(iv) Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

Solution 1

(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms 

 

(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms 

 

(iii)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms 

 

(iv)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms 

Question 2

Express each of the following in exponential form:

(i) logg 0.125 = -1

(ii) log100.01 = -2

(iii) logaA = x

(iv) log101 = 0

Solution 2

(i)

(ii)

(iii)

(iv)

Question 3

Solve for x: log10 x = -2.

Solution 3

Question 4

Find the logarithm of:

(i) 100 to the base 10

(ii) 0.1 to the base 10

(iii) 0.001 to the base 10

(iv) 32 to the base 4

(v) 0.125 to the base 2

(vi) to the base 4

(vii) 27 to the base 9

(viii) to the base 27

Solution 4

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

Question 5

State, true or false:

(i) If log10 x = a, then 10x = a.

(ii) If xy = z, then y = logzx.

(iii) log2 8 = 3 and log8 = 2 = .

Solution 5

(i)

(ii)

(iii)

Question 6

Find x, if:

(i) log3 x = 0

(ii) logx 2 = -1

(iii) log9243 = x

(iv) log5 (x - 7) = 1

(v) log432 = x - 4

(vi) log7 (2x2 - 1) = 2

Solution 6

(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

(iii)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

(iv)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

(v)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

(vi)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

Question 7

Evaluate:

(i) log10 0.01

(ii) log2 (1 ÷ 8)

(iii) log5 1

(iv) log5 125

(v) log16 8

(vi) log0.5 16

 

Solution 7

(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

(iii)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

(iv)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

(v)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

 

(vi)

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

 

Question 8

If loga m = n, express an - 1 in terms in terms of a and m.

Solution 8

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms 

Question 9

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms 

Solution 9

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms 

Question 10

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms 

Solution 10

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms

Question 11

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms 

Solution 11

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms 

Question 12

If log (x2 - 21) = 2, show that x = ± 11.

Solution 12

Selina Solutions Icse Class 9 Mathematics Chapter - Logarithms