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)

(ii)

(iii)

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 + log 125 - log 32

Solution 3

(i)

(ii)

(iii)

Question 4

Prove that:

Solution 4

Question 5

Find x, if:

x - log 48 + 3 log 2 = log 125 - log 3.

Solution 5

Question 6

Express log102 + 1 in the form of log10x.

Solution 6

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)

(ii)

(iii)

(iv)

Question 8

Solve for x:

(i)

(ii)

(iii)

(iv)

Solution 8

(i)

(ii)

(iii)

(iv)

Question 9

Given log x = m + n and log y = m - n, express the value oflog in terms of m and n.

Solution 9

Question 10

State, true or false:

(i) log 1 log 1000 = 0

(ii)

(iii) If then x = 2

(iv) log x log y = log x + log y

Solution 10

(i)

(ii)

(iii)

(iv)

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

(iv) log 5.4(v) log 60(iv) log

Solution 11

(i)

(ii)

(iii)

(iv)

(v)

(vi)

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) log 8

Solution 12

(i)

(ii)

(iii)

(iv)

(v)

(vi)

Question 13

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

(i) x(ii) log10 2x

Solution 13

(i)

(ii)

Question 14

Solution 14

Question 15

Solution 15

Question 16

Solution 16

Chapter 8 - Logarithms Exercise Ex. 8(C)

Question 1

If log10 8 = 0.90; find the value of:

(i) log10 4(ii) log

(iii) log 0.125

Solution 1

(i)

(ii)

(iii)

Question 2

If log 27 = 1.431, find the value of :

(i) log 9(ii) log 300

Solution 2

(i)

(ii)

Question 3

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

Solution 3

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

(i)

(ii)

(iii)

Question 6

Simplify:

(i) log (a)3 - log a

(ii) log (a)3 log a

Solution 6

(i)

(ii)

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 . Log (ab)

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

Solution 8

(i)

(ii)

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)

(ii)

(iii)

Question 10

Solution 10

Question 11

Solution 11

Chapter 8 - Logarithms Exercise Ex. 8(D)

Question 1

If log a + log b - 1 = 0, find the value of a9.b4.

Solution 1

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

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

(i)

(ii)

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

Question 5

If log (log a + log b), show that: a2 + b2 = 6ab.

Solution 5

Question 6

If a2 + b2 = 23ab, show that:

log (log a + log b).

Solution 6

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

Question 8

Solve for x and y ; if x > 0 and y > 0;log xy = log + 2 log 2 = 2.

Solution 8

Question 9

Find x, if:

(i) logx 625 = -4

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

Solution 9

(i)

(ii)

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

Question 13

Given log10x = 2a and log10y = .

(i) Write 10a in terms of x.

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

(iii) If , express P in terms of x and y.

Solution 13

Question 14

Solve:

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

Solution 14

Question 15

Solve for x, if:

Solution 15

Question 16

Solution 16

Question 17

Solution 17

Question 18

Solution 18

Question 19

Solution 19

Question 20

Solution 20

Question 21

Solution 21

Question 22

Solution 22

Chapter 8 - Logarithms Exercise Ex. 8(A)

Question 1

Express each of the following in logarithmic form:

(i) 53 = 125

(ii) 3-2 =

(iii) 10-3 = 0.001

(iv)

Solution 1

(i)

(ii)

(iii)

(iv)

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)

(ii)

(iii)

(iv)

(v)

(vi)

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)

(ii)

(iii)

(iv)

(v)

(vi)

Question 8

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

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

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

Solution 12

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