find the potential solution to the equation $log_{4}(2 - x) = log_{4}(-5x - 18)$. $x = square$

Explanation:

Step1: Set arguments equal

Since $\log_b(a) = \log_b(c)$ implies $a=c$ (for valid domains), we get: $2 - x = -5x - 18$

Step2: Solve for x

Isolate x terms: $-x + 5x = -18 - 2$ $4x = -20$ $\frac{4x}{4} = \frac{-20}{4}$

Answer:

$x = -5$