Question

Solve. There might be no solution or there might be 2. Check for extraneous solutions

Answer 1

14.

$\log _2(4)+\log _2(c-9)=5$

Using addition of logs property:

$\log _z(xy)=\log _z(x)+_{}\log _z(y)$$\begin{gathered} \log _2(4)+\log _2(c-9)=5 \\ \log _2(4\cdot(c-9))=5 \\ \log _2(4c-36)=5 \\ 2^{\log _2(4c-36)}=2^5 \\ 4c-36=32 \\ 4c=32+36 \\ 4c=68 \\ c=\frac{68}{4} \\ c=17 \end{gathered}$