4. For the following exercises, state the domain and range of the function.
\[
\begin{aligned}
\text { G1,G2,G3: } f(x) & =\log _{2}\left(\frac{x}{(x-2)^{2}}\right) \\
\text { G4,G5,G6: } f(x) & =\log _{3}\left(\frac{(x+1)^{2}}{(x-3)}\right) \\
\text { G7,G8,G9: } f(x) & =\log _{2}\left(\left(x^{2}-1\right)(x+1)\right) \\
\text { G10,G11,G12: } f(x) & =\log _{3}\left(\left(x^{2}-9\right)(x+4)\right)
\end{aligned}
\]
5. Find all the solutions to the given equation. If there is no solution to the equation clearly explain why.
\[
\begin{array}{l}
\text { G1,G5,G12: } \ln (y-1)=1+\ln (3 y+2) \\
\text { G2,G6,G11: } \log (w)+\log (w-21)=2 \\
\text { G3,G7,G10: } 2 \mathbf{e}^{3 y+8}-11 \mathbf{e}^{5-10 y}=0 \\
\text { G14,G8,G9: } 1-8 \ln \left(\frac{2 x-1}{7}\right)=14
\end{array}
\]
