Question

find the value of x
step by step explanation pls​

Answer 1

Answer:

The value of x is -7.

Step-by-step explanation:

The question is to find the value of x from the given equation. That is,

$\left(\dfrac{-8}{9}\right)^{2x+6}\times \left( \dfrac{-8}{9}\right) ^{3}=\left( \dfrac{-8}{9}\right) ^{x+2}$

Here the bases are the same and they are multiplied then the exponents will get added. That is, by the law of exponents we can write it as$a^{m}\times a^{n}=a^{\left( m+n\right) }$.

In this case  $a=\dfrac{-8}{9}$

Therefore,

                $\left(\dfrac{-8}{9}\right)^{2x+6}\times \left( \dfrac{-8}{9}\right) ^{3}=\left( \dfrac{-8}{9}\right) ^{x+2}\\\\\left(\dfrac{-8}{9}\right)^{2x+6+3}=\left( \dfrac{-8}{9}\right) ^{x+2}\\\\\left(\dfrac{-8}{9}\right)^{2x+9}=\left( \dfrac{-8}{9}\right) ^{x+2$

Now, equate the exponents to find the value of x.

That is,

           $2x+9=x+2\\\\2x+9-x-2=0\\\\x+7=0\\\\x=-7$

Hence the value of x is -7.

Answer 2

Answer:

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