#### Answer

$x=6$

#### Work Step by Step

Re-write the given equation as: $(2^3)^{-x+14}=(2^4)^x$
or, $2^{-3x+42}=2^{4x}$
Use the rule power rule: $a^p=a^q$.
We can see that the base $a=2$ is the same on both sides of the equation.
So, the exponents will also be equal.
This implies that $p=q$
Therefore, $ -3x+42=4x \\ 7x=42 \\ x =6$