$$\begin{aligned} & 2 ^ { x } = \frac { 1 } { 5 } \\ & 3 ^ { y } = \frac { 1 } { 4 } \end{aligned}$$
Given this, what is the value of the product $x \cdot y$?
A) $\frac { \ln 3 } { \ln 2 }$
B) $\frac { \ln 15 } { \ln 2 }$
C) $\frac { \ln 5 } { \ln 4 }$
D) $\frac { \ln 25 } { \ln 3 }$
E) $\frac { \ln 5 } { \ln 6 }$

$$4 ^ { x } \cdot 6 ^ { x } \cdot 9 ^ { x } = 36$$
Given this, what is x?
A) $\frac { 2 } { 3 }$
B) $\frac { 1 } { 4 }$
C) $\frac { 3 } { 4 }$
D) $\frac { 3 } { 8 }$
E) $\frac { 4 } { 9 }$

$$\log _ { 8 } \left( \log _ { 9 } ( \sqrt { x + 1 } ) \right) = \frac { - 2 } { 3 }$$
Given this, what is x?
A) 2
B) 3
C) 5
D) 7
E) 8

$$9 ^ { x + 1 } + 3 ^ { x + 1 } - 6 = 0$$
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) $\frac { 5 } { 4 }$

$x ^ { \ln 4 } - 6 \cdot 2 ^ { \ln x } + 8 = 0$\ What is the product of the $x$ values that satisfy this equation?\ A) $e ^ { 6 }$\ B) $e ^ { 4 }$\ C) $e ^ { 3 }$\ D) $\frac { e ^ { 2 } } { 2 }$\ E) $\frac { e ^ { 3 } } { 3 }$

Temperature conversions between Fahrenheit (${}^{\circ}\mathrm{F}$) and Celsius (${}^{\circ}\mathrm{C}$) are calculated using the formula $\mathrm{F} = \frac{9}{5} \cdot \mathrm{C} + 32$.
Cem has been assigned to measure the classroom temperature in Celsius at the same time each day for five days they go to school and find the average temperature of these five days in Celsius. On one of these five days, Cem did not go to school, and his classmate Deniz took the measurement for that day. However, Deniz mistakenly recorded the F value instead of the C value for that day's temperature in the list. Based on the values in the list, Cem calculated the average temperature for these five days as $33.8^{\circ}\mathrm{C}$.

\cline{2-6} \multicolumn{1}{c|}{}	Monday	Tuesday	Wednesday	Thursday	Friday
Temperature (${}^{\circ}\mathrm{C}$)	23	27	25	20	26

After Deniz's measured temperature value is converted to Celsius and the five-day measurement has the values in the list as shown above, on which day did Cem not go to school?
A) Monday B) Tuesday C) Wednesday D) Thursday E) Friday