Answer:
e = 1/3
Explanation:
The initial expression is:
[tex]27\log _24^{3e}=864(\frac{1}{16})[/tex]First, let's divide 864 by 16 to get:
[tex]\begin{gathered} 27\log _24^{3e}=\frac{864}{16} \\ 27\log _24^{3e}=54 \end{gathered}[/tex]Now, divide both sides by 27
[tex]\begin{gathered} \frac{27\log _24^{3e}}{27}=\frac{54}{27} \\ \log _24^{3e}=2 \end{gathered}[/tex]Then, by properties of the logarithms, the exponent of the 4 can multiply the expression as:
[tex]3e\log _24=2[/tex]Since log₂4 = 2, we get:
[tex]\begin{gathered} 3e(2)=2 \\ 6e=2 \\ \frac{6e}{6}=\frac{2}{6} \\ e=\frac{1}{3} \end{gathered}[/tex]Therefore, the value of e is 1/3
