Решение:
$\log _{0{,}4} \left(4 x + 10\right) - \log _{0{,}4} \left(0{,}2\right) = \log _{0{,}4} \left(8\right)$
$\log _{0{,}4} \left(4 x + 10\right) = \log _{0{,}4} \left(8\right) + \log _{0{,}4} \left(0{,}2\right)$
$\log _{0{,}4} \left(4 x + 10\right) = \log _{0{,}4} \left(8 \cdot 0{,}2\right)$
$\log _{0{,}4} \left(4 x + 10\right) = \log _{0{,}4} \left(1{,}6\right) .$
$4 x + 10 = 1{,}6$
$4 x = 1{,}6 - 10 = - 8{,}4$
$x = - \frac{8{,}4}{4} = - 2{,}1 .$

Ответ: -2,1

Источник: ФИПИ