SELINA Solutions for Class 9 Maths Chapter 7 - Indices (Exponents)

Evaluate:

(i)

(ii)

(iii)

(iv)

(v)

Simplify:

(i)

(ii)

(iii)

(iv)

Evaluate:

(i)

(ii)

Simplify each of the following and express with positive index:

(i)

(ii)

(iii)

(iv)

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

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

Simplify:

(i)

(ii)

Show that:

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} = 1

Simplify:

(i)

(ii)

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}

Find x, if:

(i)

(ii)

(iii)

(iv)

Solve:

(i) 4^{x - 2} - 2^{x + 1} = 0

(ii)

Solve :

(i) 8 2^2x + 4 2^x+1 = 1 + 2^x

(ii)2^2x + 2^x+2 - 4 2³ = 0

(iii)

Find the values of m and n if:

Prove that:

(i) ₌₁

 (ii)

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

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

If 5^-P = 4^-q = 20^r, show that:

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

x + y + 2 = 0

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

3^{x - 3} × 2^{3 - x}

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

9^x+2 = 720 + 9^x

Solve for x:

 4^x-1 × (0.5)^{3 - 2x} =

Solve for x:

(a^{3x + 5})². (a^x)⁴ = a^{8x + 12}

Solve for x:

Solve for x:

2^{3x + 3} = 2^{3x + 1} + 48

Solve for x:

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

Solve: 3^x-1× 5^2y-3 = 225.

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

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

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

m(n - 1) - (n - 1)