If \( \log _{2}(2 x+10)=5 \), then what is the value of \( x \) ? \( \begin{array}{ll}\text { a.) }-5 \\ \text { b.) } 10 \\ \text { c.) } 11 \\ \text { d.) }-3\end{array} \)

To solve the equation \( \log_{2}(2x + 10) = 5 \), we first rewrite it in exponential form. This gives us: \[ 2x + 10 = 2^5 \] Calculating \( 2^5 \), we find that \( 2^5 = 32 \). Therefore, we have: \[ 2x + 10 = 32 \] Next, we can isolate \( 2x \) by subtracting 10 from both sides: \[ 2x = 32 - 10 \] \[ 2x = 22 \] Now, divide both sides by 2 to find \( x \): \[ x = \frac{22}{2} = 11 \] Thus, the value of \( x \) is \( 11 \). The correct answer is \( c.) 11 \).