Answer:
Explanation:
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
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.