Question

Solve:
`((√(7))^(x) )/(7^(√(x) ) ) =7√(7)`

Answer 1

x=9

Explanation:

To simplify the expression, using only exponents:

7^((x/2)-x^(1/2)) = 7^(3/2)

x/2-x^1/2=3/2

x-2x^1/2-3=0

(x^1/2-3)(x^1/2+1)=0

x^1/2=3 as x^1/2=-1 does not have a real solution

x=9

Answer 2

x=9

Explanation:

rewriting the left half of expression: (7^1/2)^x / 7^(x^1/2)

=7^[(x/2) - (x^1/2)]

rewriting the right half: 7^(3/2)

so [(x/2) - (x^1/2)] = 3/2

x - 2x^1/2 = 3

let x=y^2, x^1/2=y

substitute y^2 - 2y -3 = 0

(y-3)(y+1)=0

y=3 or -1

x=9 or 1

put back in original expression n check

x=9 is valid but x=1 is not

ans: x=9