Answer
$x=6$
Work Step by Step
To solve the given equation, make the two sides have the same base.
Note that $8 = 2^3$ and $16=2^4$, so the given equation is equivalent to:
$(2^3)^{-x+14}=(2^4)^x$
Use the rule $(a^m)^n = a^{mn}$ to obtain:
$2^{3(-x+14)} = 2^{4x}
\\2^{-3x+42}=2^{4x}$
Use the rule $a^m=a^n \longrightarrow m=n$ to obtain:
$-3x+42=4x$
Add $3x$ to both sides of the equation to obtain:
$\begin{array}{ccc}
&-3x+42+3x &= &4x+3x
\\&42 &= &7x
\end{array}$
Divide 7 on both sides of the equation to obtain:
$\begin{array}{ccc}
&\frac{42}{7} &= &\frac{7x}{7}
\\&6 &= &x
\end{array}$
Thus, the solution set is $\left\{6\right\}$.
