(f) $\log _{2}(x+3)-\log _{4}(x+2)=1$

Step 1 ：Rewrite the equation using the change of base formula: \(\log _{2}(x+3)-\frac{\log _{2}(x+2)}{\log _{2}(4)}=1\)

Step 2 ：Simplify the equation: \(\log _{2}(x+3)-\frac{1}{2}\log _{2}(x+2)=1\)

Step 3 ：Combine the logarithms: \(\log _{2}\left(\frac{(x+3)^2}{x+2}\right)=1\)

Step 4 ：Remove the logarithm: \(\frac{(x+3)^2}{x+2}=2\)

Step 5 ：Cross-multiply: \((x+3)^2=2(x+2)\)

Step 6 ：Expand and simplify: \(x^2+6x+9=2x+4\)

Step 7 ：Move all terms to one side: \(x^2+4x+5=0\)

Step 8 ：Solve for x: \(x=-1\)

Step 9 ：\(\boxed{x=-1}\)