Question

If 27 to the power x = 9/3 to the power x, find X.

Answer 1

27^x = 9÷(3^x)
So (3^3)^x = (3^2)÷(3^x)
So 3^3x = 3^(2-x)

Comparing powers on both sides,

3x = 2 - x
So, 4x = 2
So, x = 1/2

Answer 2

Hi ,

Here we use laws of exponents :

Given ( 27 ) ^ x = 9 / 3 ^x

⇒ ( 3 × 3 × 3 )^x = ( 3 × 3 ) / 3^x

⇒ ( 3 ³ )^x = 3² / 3^x

⇒  3 ^ 3x × 3^x = 3²            [ since  ( a ^m)^n = a ^mn ]

⇒ 3^ (3x +x) = 3²                [ since a^m × a^n = a ^m+n ]

⇒ 3^4x = 3²

⇒4x = 2                      [ since  If a ^m = a ^n then m = n ]

⇒ x = 2 / 4

  ∴ x = 1 / 2

I hope this helps you.

*****