The power of x
Find the value of $x$ in this equation, where it appears in powers.
Problem
Student Solutions
Answer: $x=3$
Using numbers
$x-1$ and $x+1$ are $2$ apart
Powers of $2$ (two columns so that numbers above each other are $2$ powers apart):
$2$ $4$
$8$ $16$ $4$ and $16$ are $12$ apart
$32$ $64$ numbers are getting too far apart
$16-4=12$
$2^4-2^2=12$
$x=3$
Using index laws
$2^{x+1}=2^x\times2^1=2^x\times2$ and $2^{x-1}=2^x\times2^{-1}=2^x\times\frac12$.
Substitute then factorise: