Answer:
The solution will be "x = 2 and x = -1".
Step-by-step explanation:
The given equation is:
⇒ [tex]2^{2x+2}\times 5^{x-1}=8^x\times 5^{2x}[/tex]
On solving "[tex]8^x[/tex]", we get
⇒ [tex]2^{2x+2}\times 5^{x-1}=(2^3)^x\times 5^{2x}[/tex]
As we know, if the base are same then their powers will be added together.
⇒ [tex]2x+2=3x[/tex] ...(equation 1)
⇒ [tex]x-1=2x[/tex] ...(equation 2)
From equation 1, we get
⇒ [tex]2=3x-2x[/tex]
⇒ [tex]2=x \ i.e., x =2[/tex]
From equation 2, we get
⇒ [tex]-1=2x-x[/tex]
⇒ [tex]-1=x \ i.e., x=-1[/tex]
So that the correct answer will be "x = 2" and "x = -1".
