English Medium इयत्ता ९ - CBSE Question Bank Solutions

If `5^(3x)=125` and `10^y=0.001,` find x and y.

Solve the following equation:

`3^(x+1)=27xx3^4`

Solve the following equation:

`4^(2x)=(root3 16)^(-6/y)=(sqrt8)^2`

Solve the following equation:

`3^(x-1)xx5^(2y-3)=225`

Solve the following equation:

`8^(x+1)=16^(y+2)` and, `(1/2)^(3+x)=(1/4)^(3y)`

Solve the following equation:

`4^(x-1)xx(0.5)^(3-2x)=(1/8)^x`

Solve the following equation:

`sqrt(a/b)=(b/a)^(1-2x),` where a and b are distinct primes.

If a and b are distinct primes such that `root3 (a^6b^-4)=a^xb^(2y),` find x and y.

If a and b are different positive primes such that

`((a^-1b^2)/(a^2b^-4))^7div((a^3b^-5)/(a^-2b^3))=a^xb^y,` find x and y.

If a and b are different positive primes such that

`(a+b)^-1(a^-1+b^-1)=a^xb^y,` find x + y + 2.

If `2^x xx3^yxx5^z=2160,` find x, y and z. Hence, compute the value of `3^x xx2^-yxx5^-z.`

If 1176 = `2^axx3^bxx7^c,` find the values of a, b and c. Hence, compute the value of `2^axx3^bxx7^-c` as a fraction.

Simplify:

`(x^(a+b)/x^c)^(a-b)(x^(b+c)/x^a)^(b-c)(x^(c+a)/x^b)^(c-a)`

Simplify:

`root(lm)(x^l/x^m)xxroot(mn)(x^m/x^n)xxroot(nl)(x^n/x^l)`

Show that:

`((a+1/b)^mxx(a-1/b)^n)/((b+1/a)^mxx(b-1/a)^n)=(a/b)^(m+n)`

If `a=x^(m+n)y^l, b=x^(n+l)y^m` and `c=x^(l+m)y^n,` Prove that `a^(m-n)b^(n-l)c^(l-m)=1`

If `x = a^(m + n), y = a^(n + l)` and `z = a^(l + m),` prove that `x^my^nz^l = x^ny^lz^m`

Evaluate the following using identities:

`(2x+ 1/x)^2`

Evaluate the following using identities:

(2x + y) (2x − y)

Evaluate the following using identities:

`(a^2b - b^2a)^2`