Question: Solve the following equations exactly.

a. \[{{\log }_{2}}(x+3)=1+{{\log }_{2}}(x-2)\]

b. \[{{e}^{2x}}-9-8{{e}^{x}}=0\] c. \[\ln (x+6)-\ln (x-4)=\ln x\]

d. \(4\left( {{7}^{x}} \right)=72\) e. \(\frac{-2}{3}\ln (1-2x)=-2\)