Question

Find the value of x,if 2^2x+2=4^2x-1

Answer 1

hii

2^(2x+2) =2^{2(2x-1)}

2^(2x+2)=2^(4x-2)


if the bases are same , powers are equal

2x+2=4x-2

4=4x-2x

4=2x

4/2=x

x=2

Answer 2

Given:

We have given an equation which is  $2^{2x+2}=4^{2x-1}$.

To Find:

We have to find the value of x?

Step-by-step explanation:

• An equation is given to us which is written below for simplifying the given equation we will follow the steps.

      $2^{2x+2}=4^{2x-1}$

• First of all in the right-hand side we will right the value of 4 as a square format which is written as.

      $2^{2x+2}=2^(2^{2x-1})$

• Now simplify the right-hand side bracket which will give

       $2^{2x+2}=2^{4x-2}$

• We will use the basic concept here which says if the base of power is equal then the power will also be equal.

       $a^n=b^m,\Rightarrow n=m$

• Comparing the formula with the above equation we get the result

       $2x+2=4x-2$

• Now take the like terms together and simplify them

        $2x-4x=-2-2\\-2x=-4\\x=2$

Hence, the value of x is 2.