Answer:
A&D
Step-by-step explanation:
we want to solve the following equation for x:
[tex] \displaystyle ( {2}^{x} - 3) ({2}^{x} - 4) = 0[/tex]
to do so let [tex]2^x[/tex] be u and transform the equation:
[tex] \displaystyle (u - 3) (u - 4) = 0[/tex]
By Zero product property we obtain:
[tex] \displaystyle \begin{cases}u - 3 = 0\\ u - 4= 0 \end{cases}[/tex]
Solve the equation for u which yields:
[tex] \displaystyle \begin{cases}u = 3\\ u = 4 \end{cases}[/tex]
substitute back:
[tex] \displaystyle \begin{cases} {2}^{x} = 3\\ {2}^{x} = 4 \end{cases}[/tex]
take logarithm of Base 2 in both sides of the both equations:
[tex] \displaystyle \begin{cases} \log_{2} {2}^{x} = \log_{2} 3\\ \log_{2} {2}^{x} = \log_{2} 4 \end{cases}[/tex]
hence,
[tex] \displaystyle \begin{cases} x_{1} = \log_{2} 3\\ x_{2} = 2 \end{cases}[/tex]
