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

Solve for x:
2^2x + 2^{x +2} - 4 x 2³ = 0

Solve for x:

9 x 81^x = `(1)/(27^(x - 3)`

Solve for x:
2^{2x- 1} − 9 x 2^{x − 2} + 1 = 0

Solve for x:
5^x2 : 5^x = 25 : 1

Solve for x:

`sqrt((8^0 + 2/3)` = (0.6)^2-3x 

Solve for x:

`sqrt((3/5)^(x + 3)) = (27^-1)/(125^-1)`

Solve for x:
9^x+4 = 3² x (27)^x+1

Find the value of k in each of the following:

`(root(3)(8))^((-1)/(2)` = 2^k 

Find the value of k in each of the following:

`root(4)root(3)(x^2)` = x^k 

Find the value of k in each of the following:

`(sqrt(9))^-7 xx (sqrt(3))^-5` = 3^k 

Find the value of k in each of the following:

`(1/3)^-4 ÷ 9^((-1)/(3)` = 3^k 

If a = `2^(1/3) - 2^((-1)/3)`, prove that 2a³ + 6a = 3

If x = `3^(2/3) + 3^(1/3)`, prove that x³ - 9x - 12 = 0

If `root(x)("a") = root(y)("b") = root(z)("c")` and abc = 1, prove that x + y + z = 0

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

Show that : `(1)/(1 + "a"^("p"- "q")) + (1)/(1 + "a"^("q"- "p")`

Find the value of (8p)^p if 9^{p + 2} - 9^p = 240.

If a^x = b^y = c^z and abc = 1, show that

`(1)/x + (1)/y + (1)/z` = 0.

If `x^(1/3) + y^(1/3) + z^(1/3) = 0`, prove that (x + y + z)³ = 27xyz

If 2250 = 2^a. 3^b. 5^c, find a, b and c. Hence, calculate the value of 3^a x 2^-b x 5^-c.