Question

Year 10 mathematics GCSE

Answer 1

The answer is x= -9

Step by step explanation:

To find x.

Writing every term on the left hand side in the form of 3.

`(18*(3*√(3))^(4n+6))/(6*3^(2(2n+8)) )=3^(x)`

`(3 * (3*3)^(2n+3) )/(3^(4n+16) )=3^(x)`

`(3*3^(4n+6) )/(3^(4n+16) )=3^(x)`

`\frac{3^(4n+7) } {3^(4n+16) } =3^(x)`

`3^(-9) =3^(x)`

On comparing the equation,

x= -9

Answer 2

• 
  `x=2n-6`

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Solve the given equation in below steps:

• 
  `\cfrac{18*(√(27) )^(4n+6)}{6*9^(2n+8)}=3^x`
• 
  `\cfrac{3*(√(3^3) )^(4n+6)}{(3^2)^(2n+8)}=3^x`
• 
  `\cfrac{3*(3^(3/2) )^(4n+6)}{3^(4n+16)}=3^x`
• 
  `3^(1+3(2n+3)-4n-16)=3^x`
• 
  `3^(1+6n+9-4n-16)=3^x`
• 
  `3^(2n-6)=3^x`
• 
  `x=2n-6`