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

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`

Find the values of m and n if : 
`4^(2m) = ( root(3)(16))^(-6/n) = (sqrt8)^2`

Solve x and y if : ( √32 )^x ÷ 2^{y + 1} = 1 and 8^y - 16^{4 - x/2} = 0

Evaluate : `[(-2/3)^-2]^3 xx (1/3)^-4 xx 3^-1 xx 1/6`

Simplify : `[ 3 xx 9^( n + 1 ) - 9 xx 3^(2n)]/[3 xx 3^(2n + 3) - 9^(n + 1 )]`

Solve : 3^x-1× 5^2y-3 = 225.

If `((a^-1b^2 )/(a^2b^-4))^7 ÷ (( a^3b^-5)/(a^-2b^3))^-5 = a^x . b^y` , find x + y.

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