Question

(11/9)^3 × (9/11)^6 = (11/9)^2x-1
Pls find the value of x

Answer 1

Step-by-step explanation:

Given: (11/9)3 × (9/11)6 = (11/9)2x-1

The multiplier of L.H.S of the equation can be written as:

(11/9)3 × (11/9)-6 = (11/9)2x-1

⇒ (11/9)3-6 = (11/9)2x-1

Therefore, -3 = 2x – 1

2x = -3 + 1

x = -2/2

x = -1

Answer 2

Given,

(11/9)^3 × (9/11)^6 = (11/9)^2x-1

To Find,

The value of x =?

Solution,

We can solve the question using the following steps:

Considering the given equation,

$(\frac{11}{9})^{3} * (\frac{9}{11})^{6} = (\frac{11}{9})^{2x - 1}$

Now, we will invert the second term so that the base is the same on the LHS. When we invert a fraction, the power becomes negative.

⇒$(\frac{11}{9})^{3} * (\frac{11}{9})^{-6} = (\frac{11}{9})^{2x - 1}$

⇒$(\frac{11}{9})^{3 + (-6)} = (\frac{11}{9})^{2x - 1}$       (Since the base is the same on the LHS)

⇒$(\frac{11}{9})^{-3} = (\frac{11}{9})^{2x - 1}$

Since the base is equal on both sides, we can equate their exponents.

$-3 = 2x - 1$

$-2 = 2x$

$x = -1$

Hence, the value of x is -1.