If (9/7)³ × (49/81)^(2x-6) = (7/9)⁹, What is the value of x?

To prove this equation true we will use exponential power identity.

Answer: If (9/7)³ × (49/81)^(2x-6) = (7/9)⁹ then value of x is 6

Here's the solution.

Explanation:

⇒ (9/7)³ × (49/81)^(2x-6) = (7/9)⁹

We can write (9/7)³ as (7/9)^-3

⇒ (7/9) ^-3 × [ (7/9)² ] ^(2x-6) = (7/9)⁹

We know that x^a + x^b  = a + b 

⇒ (7/9) ^-3 × (7/9) ^(4x-12) = (7/9)⁹  

As we know that the base is same, so we can add the powers.

⇒ - 3 + 4 x - 12 = 9

⇒ 4 x - 15 = 9

⇒ 4 x = 9 +15

⇒ 4 x = 24

⇒ x = 6

Thus, if (9/7)³ × (49/81)^(2x-6) = (7/9)⁹ then value of x is 6.