Solve for $x$. Round to 2 decimal places. \[ 4-3^{x-7}=15 \]

Step 1 ：First, we isolate the term with the variable $x$ by subtracting $4$ from both sides of the equation. This gives us $-3^{x-7}=15-4$.

Step 2 ：Simplify the right side of the equation to get $-3^{x-7}=11$.

Step 3 ：Next, we get rid of the negative sign on the left side by multiplying both sides of the equation by $-1$. This gives us $3^{x-7}=-11$.

Step 4 ：Since we cannot have a negative number equal to a power of $3$, there are no solutions to this equation.