ICSE Class 9 Logarithms Solution New Pattern

## ICSE Class 9 Logarithms Solution New Pattern By Clarify Knowledge

ICSE Class 9 Logarithms Solution New Pattern 2022

## 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 = 0Solution 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 27Solution 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) = 2Solution 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 16Solution 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

## 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 3Solution 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 32Solution 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 3Solution 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 ySolution 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 8Solution 12

(i)

(ii)

(iii)

(iv)

(v)

(vi)

Question 13

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

(i) x(ii) log10 2xSolution 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 0.125Solution 1

(i)

(ii)

(iii)

Question 2

If log 27 = 1.431, find the value of :

(i) log 9(ii) log 300Solution 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 aSolution 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 = 10Solution 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 - zSolution 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: a+ 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) = 2Solution 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

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