Question

find the potential solution to the equation \\(\log_{4}(2 - x)=\log_{4}(-5x - 18)\\)\\(x = \boxed{}\\)

Explanation:

Step1: Set arguments equal

Since $\log_b(a) = \log_b(c)$ implies $a=c$ (for $b>0, b
eq1$), we set:
$2 - x = -5x - 18$

Step2: Isolate $x$ terms

Add $5x$ to both sides:
$2 + 4x = -18$

Step3: Isolate constant terms

Subtract 2 from both sides:
$4x = -20$

Step4: Solve for $x$

Divide by 4:
$x = \frac{-20}{4} = -5$

Step5: Verify domain

Check arguments are positive:
$2 - (-5) = 7 > 0$, $-5(-5) - 18 = 25 - 18 = 7 > 0$. Both are valid.

Answer:

$-5$