$$9 ^ { x + 1 } + 3 ^ { x + 1 } - 6 = 0$$
Given this, which of the following is x?
A) $\frac { \ln 3 } { \ln 2 }$
B) $\frac { 1 + \ln 3 } { \ln 2 }$
C) $\frac { 2 + \ln 3 } { \ln 2 }$
D) $\frac { 3 + \ln 2 } { \ln 3 }$
E) $\frac { \ln 2 - \ln 3 } { \ln 3 }$

$$4 ^ { x - 2 } = 6 ^ { 2 x - 2 }$$
Given that, what is the value of the expression $9 ^ { \mathbf { x } }$?
A) $\frac { 9 } { 2 }$
B) $\frac { 4 } { 3 }$
C) $\frac { 8 } { 3 }$
D) $\frac { 5 } { 4 }$
E) $\frac { 9 } { 4 }$

$$3 ^ { x } \cdot 12 ^ { 2 - x } = 18$$
Given this, what is $x$?
A) $\frac { 1 } { 2 }$
B) $\frac { 3 } { 2 }$
C) $\frac { 1 } { 3 }$
D) $\frac { 4 } { 3 }$
E) $\frac { 5 } { 4 }$