How do i solve 5 times 2 to the power of x minus 2

What is best way to getting answer for my exam is

Jack has a piece of red ribbon that is two times as long as his piece of blue ribbon. he says that he can use two different equation to find out how long his piece of red ribbon is compared to his piece of blue ribbon is. is he correct? explain his reasoning

Can someone check if i did this right since i really want to make sure it’s correct. if you do you so much