Powers of Four
Can you work out the value of x in this 'power-full' equation?
Age
14 to 16
Challenge level
Problem
If $4^x+4^x+4^x+4^x = 4^{16}$, what is the value of $x$?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Answer: 15
$4^x+4^x+4^x+4^x = 4 \times 4^x$ = $4^{x+1}$
So $x+1=16$, hence $x = 15$