Question

Find x if (2/3) raise to 2 multiply by (2/3)raise to9 = (2/3)raise to3x plus 2​

Answer 1

Answer:

Step-by-step explanation:

Given that,

2/3)² × (2/3) power 9 = (2/3) power (3x +2)

⇒ (2/3) power (2+9) = (2=3) power (3x +2) (∵ Bases are equal then powers should be add )

⇒ (2/3)power (11) = (2/3)power (3x +2)

⇒ 11 = 3x +2 ( ∵ Bases are equal then powers should be equal )

⇒ 11 - 2 = 3x ( ∵ transposing )

⇒ 9 = 3x

⇒ 9/3 = x ( ∵ transposing )

⇒ 3 = x

Hence, x = 3 is the answer.

Answer 2

Answer:

The value of $x=3$

Step-by-step explanation:

Given expression is,

$(\frac{2}{3}) ^{2} *(\frac{2}{3} )^{9} =(\frac{2}{3})^{3x+2}$

To find : The value of $x$.

Solution :

• The given expression is,

         $(\frac{2}{3} )^{2}*(\frac{2}{3} )^{9} = (\frac{2}{3})^{3x+2}$

• As we can see that the base of all the terms is equal.
• We know the property of fractional numbers that "if the bases are same, the powers can be added."
• Applying this property to the given equation, we get

                    $2+9 = 3x+2$

• On solving, we get

                        $11 = 3x+2$

                     ∴ $3x = 11-2$

                       ∴ $x = \frac{9}{3}$

                        ∴ $x = 3$

• The value of $x=3$.