ICSE Class 9 Indices Solution New Pattern By Clarify Knowledge

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ICSE Class 9 Indices Solution Table

Chapter 7 - Indices (Exponents) Exercise Ex. 7(A)

Question 1

Evaluate:

(i) 

(ii) 

(iii) 

(iv) 

(v) Solution 1

(i)

(ii)

(iii)

(iv)

(v)

Question 2

Simplify:

(i) 

(ii) 

(iii) 

(iv) Solution 2

(i)

(ii)

(iii)

(iv)

Question 3

Evaluate:

(i) 

(ii) Solution 3

(i)

(ii)

Question 4

Simplify each of the following and express with positive index:

(i) 

(ii) 

(iii) 

(iv) Solution 4

(i)

(ii)

(iii)

(iv)

Question 5

If 2160 = 2^a. 3^b. 5^c, find a, b and c. Hence calculate the value of 3^a 2^-b 5^-c.Solution 5

Question 6

If 1960 = 2^a. 5^b. 7^c, calculate the value of 2^-a. 7^b. 5^-c.Solution 6

Question 7

Simplify:

(i) 

(ii) Solution 7

(i)

(ii)

Question 8

Show that:

Solution 8

Question 9

If a = x^{m + n}. y^l; b = x^n + l. l ^. y^m and c = x^{l + m}. yⁿ,

Prove that: a^{m - n}. b^n - l. c^{l - m} = 1Solution 9

Question 10

Simplify:

(i) 

(ii) Solution 10

(i)

(ii)

Chapter 7 - Indices (Exponents) Exercise Ex. 7(B)

Question 1

Solve for x:

(i) 2^2x+1 = 8

(ii) 2^5x-1 = 4 2^{3x + 1}

(iii) 3^{4x + 1} = (27)^{x + 1}

(iv) (49)^{x + 4} = 7² (343)^{x + 1}Solution 1

(i)

(ii)

(iii)

(iv)

Question 2

Find x, if:

(i) 

(ii) 

(iii) 

(iv) Solution 2

(i)

(ii)

_(iii)

_(iv)

Question 3

Solve:

(i) 4^{x - 2} - 2^{x + 1} = 0

(ii) Solution 3

(i)

(ii)

Question 4

Solve :

(i) 8 2^2x + 4 2^x+1 = 1 + 2^x

(ii)2^2x + 2^x+2 - 4 2³ = 0

(iii) Solution 4

(i)

(ii)

(iii)

Question 5

Find the values of m and n if:

Solution 5

Question 6

Solution 6

Question 7

Prove that:

(i) ₌₁

 (ii) Solution 7

(i)

_(ii)

Question 8

If a^x = b, b^y = c and c^z = a, prove that: xyz = 1.Solution 8

Question 9

If a^x = b^y = c^z and b² = ac, prove that : Solution 9

Question 10

If 5^-P = 4^-q = 20^r, show that:

Solution 10

Question 11

If m ≠ n and (m + n)^-1 (m^-1 + n^-1) = m^xn^y, show that:

x + y + 2 = 0Solution 11

Question 12

If 5^{x + 1} = 25^{x - 2}, find the value of

3^{x - 3} × 2^{3 - x}Solution 12

Question 13

If 4^{x + 3} = 112 + 8 × 4^x, find the value of (18x)^3x.Solution 13

Question 14 (i)

Solve for x:

 4^x-1 × (0.5)^{3 - 2x} = Solution 14 (i)

Question 14 (ii)

Solve for x:

(a^{3x + 5})². (a^x)⁴ = a^{8x + 12}Solution 14 (ii)

Question 14 (iii)

Solve for x:

Solution 14 (iii)

Question 14 (iv)

Solve for x:

2^{3x + 3} = 2^{3x + 1} + 48Solution 14 (iv)

Question 14 (v)

Solve for x:

3(2^x + 1) - 2^{x + 2} + 5 = 0Solution 14 (v)

Question 14 (vi)

9^x+2 = 720 + 9^xSolution 14 (vi)

9^x+2 = 720 + 9^x

⇒ 9^x+2 - 9^x = 720

⇒ 9^x (9² - 1) = 720

⇒ 9^x (81 - 1) = 720

⇒ 9^x (80) = 720

⇒ 9^x = 9

⇒ 9^x = 9¹

⇒ x = 1

Chapter 7 - Indices (Exponents) Exercise Ex. 7(C)

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solve: 3^x-1× 5^2y-3 = 225.Solution 3

Question 4

Solution 4

Question 5

If 3^x+1 = 9^x-3, find the value of 2^1+x.Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solve: 3(2^x + 1) - 2^x+2 + 5 = 0.Solution 10

Question 11

If (a^m)ⁿ = a^m .aⁿ, find the value of:

m(n - 1) - (n - 1)Solution 11

Question 12

Solution 12

Question 13

Solution 13

Question 14

Solution 14

Question 15 (i)

Solution 15 (i)

Question 15 (ii)

Solution 15 (ii)

Question 16

Solution 16