Question

calculate the value of 'X' in the following expressions :
(11/9)^3 * (11/9)^6 = (11/9)^2x-1​

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

by-- prince

Answer 2

Answer:

The value of x is 5.

Step-by-step-explanation:

We have given that,

$\displaystyle{\sf\:\left(\:\dfrac{11}{9}\:\right)^3\:\times\:\left(\:\dfrac{11}{9}\:\right)^6\:=\:\left(\:\dfrac{11}{9}\:\right)^{2x\:-\:1}}$

We have to find the value of x.

Now,

$\displaystyle{\sf\:\left(\:\dfrac{11}{9}\:\right)^3\:\times\:\left(\:\dfrac{11}{9}\:\right)^6\:=\:\left(\:\dfrac{11}{9}\:\right)^{2x\:-\:1}}$

$\displaystyle{\implies\sf\:\left(\:\dfrac{11}{9}\:\right)^{3\:+\:6}\:=\:\left(\:\dfrac{11}{9}\:\right)^{2x\:-\:1}\:\qquad\dots\:[\:a^m\:\times\:a^n\:=\:a^{m\:+\:n}\:]}$

$\displaystyle{\implies\sf\:3\:+\:6\:=\:2x\:-\:1\:\qquad\dots\:[\:Bases\:are\:equal\:]}$

$\displaystyle{\implies\sf\:9\:=\:2x\:-\:1}$

$\displaystyle{\implies\sf\:2x\:=\:9\:+\:1}$

$\displaystyle{\implies\sf\:2x\:=\:10}$

$\displaystyle{\implies\sf\:x\:=\:\cancel{\dfrac{10}{2}}}$

$\displaystyle{\implies\underline{\boxed{\red{\sf\:x\:=\:5\:}}}}$

∴ The value of x is 5.