tmua 2021 Q14

tmua · Uk · paper2 1 marks Exponential Functions Exponential Equation Solving
Consider the following simultaneous equations, where $p$ is a real number:
$$\begin{array} { r } p 2 ^ { x } + \log _ { 2 } y = 2 \\ 2 ^ { x } + \log _ { 2 } y = 1 \end{array}$$
What is the complete range of $p$ for which these simultaneous equations have a real solution $( x , y )$ ?
A $p < 1$
B $p \neq 1$
C $p > 1$
D $p < 1$ or $p > 2$
E $\quad p \neq 1$ and $p < 2$ F $p > 1$ and $p < 2$ G $p > 2$ H All real values of $p$
..... 16
Consider the following simultaneous equations, where $p$ is a real number:

$$\begin{array} { r } 
p 2 ^ { x } + \log _ { 2 } y = 2 \\
2 ^ { x } + \log _ { 2 } y = 1
\end{array}$$

What is the complete range of $p$ for which these simultaneous equations have a real solution $( x , y )$ ?

A $p < 1$\\
B $p \neq 1$\\
C $p > 1$\\
D $p < 1$ or $p > 2$\\
E $\quad p \neq 1$ and $p < 2$\\
F $p > 1$ and $p < 2$\\
G $p > 2$\\
H All real values of $p$