English Medium Class 9 - CBSE Question Bank Solutions for Mathematics

Prove that:

`(2^n+2^(n-1))/(2^(n+1)-2^n)=3/2`

Prove that:

`(64/125)^(-2/3)+1/(256/625)^(1/4)+(sqrt25/root3 64)=65/16`

Prove that:

`(3^-3xx6^2xxsqrt98)/(5^2xxroot3(1/25)xx(15)^(-4/3)xx3^(1/3))=28sqrt2`

Prove that:

`((0.6)^0-(0.1)^-1)/((3/8)^-1(3/2)^3+((-1)/3)^-1)=(-3)/2`

Show that:

`1/(1+x^(a-b))+1/(1+x^(b-a))=1`

Show that:

`[{x^(a(a-b))/x^(a(a+b))}div{x^(b(b-a))/x^(b(b+a))}]^(a+b)=1`

Show that:

`(x^(1/(a-b)))^(1/(a-c))(x^(1/(b-c)))^(1/(b-a))(x^(1/(c-a)))^(1/(c-b))=1`

Show that:

`(x^(a^2+b^2)/x^(ab))^(a+b)(x^(b^2+c^2)/x^(bc))^(b+c)(x^(c^2+a^2)/x^(ac))^(a+c)=x^(2(a^3+b^3+c^3))`

Show that:

`(x^(a-b))^(a+b)(x^(b-c))^(b+c)(x^(c-a))^(c+a)=1`

Show that:

`{(x^(a-a^-1))^(1/(a-1))}^(a/(a+1))=x`

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`