The power of x

Find the value of $x$ in this equation, where it appears in powers.

Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative


Find the value of $x$, where $$2^{x+1}-2^{x-1}=12$$

This problem is adapted from the World Mathematics Championships