\begin{tabular}{l} Solve for $$ x $$ \ $$ \qquad \log _{4}(-2 x+11)=2 $$ \ $$ x=\square $$ \ \hline$$ \frac{\square}{\square} $$ \ \hline\end{tabular}

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UpStudy AI · Accepted Answer

Given the equation
$$
\log_{4}(-2x + 11) = 2,
$$
we convert it to its exponential form. Recall that if 
$$
\log_{a}(b) = c,
$$
then 
$$
b = a^{c}.
$$
Thus,
$$
-2x + 11 = 4^2.
$$

Since
$$
4^2 = 16,
$$
we have
$$
-2x + 11 = 16.
$$

Subtract $$11$$ from both sides:
$$
-2x = 16 - 11,
$$
which simplifies to
$$
-2x = 5.
$$

Divide both sides by $$-2$$ to solve for $$x$$:
$$
x = -\frac{5}{2}.
$$

Thus, the solution is
$$
x = -\frac{5}{2}.
$$
$$ x = -\frac{5}{2} $$

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