Question

2^2x+2 *5^x-1=8^x*5^2x

Answer 1

The solution will be "x = 2 and x = -1".

Explanation:

The given equation is:

⇒
`2^(2x+2)* 5^(x-1)=8^x* 5^(2x)`

On solving "
`8^x`", we get

⇒
`2^(2x+2)* 5^(x-1)=(2^3)^x* 5^(2x)`

As we know, if the base are same then their powers will be added together.

⇒
`2x+2=3x` ...(equation 1)

⇒
`x-1=2x` ...(equation 2)

From equation 1, we get

⇒
`2=3x-2x`

⇒
`2=x \ i.e., x =2`

From equation 2, we get

⇒
`-1=2x-x`

⇒
`-1=x \ i.e., x=-1`

So that the correct answer will be "x = 2" and "x = -1".