6. Find algebraically the exact solutions to the equations
- \(\ln ( 4 - 2 x ) + \ln ( 9 - 3 x ) = 2 \ln ( x + 1 ) , \quad - 1 < x < 2\)
- \(2 ^ { x } \mathrm { e } ^ { 3 x + 1 } = 10\)
Give your answer to (b) in the form \(\frac { a + \ln b } { c + \ln d }\) where \(a , b , c\) and \(d\) are integers.