(English Medium) ICSE Class 9 - CISCE Question Bank Solutions

Find x, if : `(root(3)( 2/3))^( x - 1 ) = 27/8`

Solve :  4^{x - 2} - 2^{x + 1} = 0

Solve : `[3^x]^2` : 3x = 9 : 1

Solve : 8 x 2^2x + 4 x 2^{x + 1} = 1 + 2^x

Solve: 

2^2x + 2^x+2 − 4 × 2³ = 0

Solve : `(sqrt(3))^( x - 3 ) = ( root(4)(3))^( x + 1 )`

Solve for x : 9^x+2 = 720 + 9^x

Solve for x: `4^(x-1) × (0.5)^(3 - 2x) = (1/8)^-x`

Solve for x :  (a^{3x + 5})². (a^x)⁴ = a^{8x + 12}

Solve for x: 

`(81)^(3/4) - (1/32)^(-2/5) + x(1/2)^(-1).2^0 = 27`

Solve for x:

`2^(3x  +  3) = 2^(3x  +  1) + 48`

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

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

If 5^{x + 1} = 25^{x - 2}, find the value of  3^{x - 3} × 2^{3 - x}.

If m ≠ n and (m + n)^-1 (m^-1 + n^-1) = m^xn^y, show that : x + y + 2 = 0

If 5^-P = 4^-q = 20^r, show that : `1/p + 1/q + 1/r = 0`

If a^x = b^y = c^z and b² = ac, prove that: y = `[2xz]/[x + z]`

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

Prove that : `((x^a)/(x^b))^( a + b - c ) (( x^b)/(x^c))^( b + c - a )((x^c)/(x^a))^( c + a - b)`

Prove that :
`[ x^(a(b - c))]/[x^b(a - c)] ÷ ((x^b)/(x^a))^c = 1`