Answer
$\displaystyle \{\frac{0.5-\log_{4}3}{0.2}\}$ or $\{-1.462\}$
Work Step by Step
... Divide with $0.3$
$4^{0.2x}=\displaystyle \frac{2}{3} \quad $... Apply $\log_{4}$(...) to both sides
... LHS: $\log_{4}4^{0.2x}=0.2x\log_{4}4=0.2x(1)=0.2x$
... RHS: $\displaystyle \log_{4}\frac{2}{3}=\log_{4}2-\log_{4}3=\log_{4}4^{1/2}-\log_{4}3=0.5-\log_{4}3$
$0.2x=0.5-\log_{4}3$
$x=\displaystyle \frac{0.5-\log_{4}3}{0.2}\approx-1.462$
Solution set: $\displaystyle \{\frac{0.5-\log_{4}3}{0.2}\}$ or $\{-1.462\}$
