English Medium कक्षा ९ - CBSE Question Bank Solutions

Show that:

`(a^(x+1)/a^(y+1))^(x+y)(a^(y+2)/a^(z+2))^(y+z)(a^(z+3)/a^(x+3))^(z+x)=1`

Show that:

`(3^a/3^b)^(a+b)(3^b/3^c)^(b+c)(3^c/3^a)^(c+a)=1`

If 2^x = 3^y = 12^z, show that `1/z=1/y+2/x`

If 2^x = 3^y = 6^-z, show that `1/x+1/y+1/z=0`

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

If 3^x = 5^y = (75)^z, show that `z=(xy)/(2x+y)`

If `27^x=9/3^x,` find x.

Find the value of x in the following:

`2^(5x)div2x=root5(2^20)`

Find the value of x in the following:

`(2^3)^4=(2^2)^x`

Find the value of x in the following:

`(3/5)^x(5/3)^(2x)=125/27`

Find the value of x in the following:

`5^(x-2)xx3^(2x-3)=135`

Find the value of x in the following:

`2^(x-7)xx5^(x-4)=1250`

Find the value of x in the following:

`(root3 4)^(2x+1/2)=1/32`

Find the value of x in the following:

`5^(2x+3)=1`

Find the value of x in the following:

`(13)^(sqrtx)=4^4-3^4-6`

Find the value of x in the following:

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

If `x=2^(1/3)+2^(2/3),` Show that x³ - 6x = 6

Determine `(8x)^x,`If `9^(x+2)=240+9^x`

If `3^(x+1)=9^(x-2),` find the value of `2^(1+x)`

If `3^(4x) = (81)^-1` and `10^(1/y)=0.0001,` find the value of `  2^(-x+4y)`.