Answer
The solution set is $\{\log_{4}5\}$ or $\{1.161\}$
Work Step by Step
... Substitute $t=4^{x}$ (t is positive)
... the equation becomes
$t-10\displaystyle \cdot\frac{1}{t}-3=0 \quad $... multiply with t
$t^{2}-10-3t=0 \quad $... rewrite, in order of powers
$t^{2}-3t-10=0 \quad $
... two factors of $-10$ whose sum is $-3$ ... are $-5$ and $+2$
$(t-5)(t+2)=0\quad \Rightarrow\quad t=5$ or $t=-2$
... Since t must be positive, discard the $t=-2$ solution.
... Bring back x
$t=5$
$4^{x}=5 \quad $...Apply$: \quad \log_{4}(...)$
$x=\log_{4}5\approx 1.161$
The solution set is $\{\log_{4}5\}$ or $\{1.161\}$
