Solve for $x$: $2^{x-3}=4^{x+1}$
Using the exponent rules, I get $2^{x-3}=2^{2(x+1)}$. Now that both sides have the same base, I can equate the exponents and solve for $x$. I get $x-3=2(x+1)$, which simplifies to $x-3=2x+2$. Subtracting $x$ from both sides, I get $-3=x+2$. Subtracting 2 from both sides, I get $-5=x$. 