Answer:
[tex]\begin{gathered} a)\text{ True} \\ b)\text{ False} \\ c)\text{ False} \end{gathered}[/tex]
Explanation:
Here, we want to get the value of the logarithmic or exponential expression
a)
[tex]\begin{gathered} The\text{ general rule here is:} \\ a^{log\placeholder{⬚}_ab}\text{ = b} \\ \\ Thus: \\ 2^{4log\placeholder{⬚}_23}\text{ = 2}^{log\placeholder{⬚}_23^4}\text{ = 2}^{log\placeholder{⬚}_281}\text{ = 81} \end{gathered}[/tex]
Thus, the above statement is true
b)
[tex]\begin{gathered} ln\text{ e}^{\frac{3}{2}} \\ =\text{ }\frac{3}{2}ln\text{ e} \\ ln\text{ e = 1} \\ =\text{ }\frac{3}{2}\times1\text{ = }\frac{3}{2} \end{gathered}[/tex]
The above is false
c)
[tex]\begin{gathered} 2ln\text{ e = 2} \\ we\text{ now have} \\ e^{3+2}\text{ = e}^5 \end{gathered}[/tex]
This means that the above statement is false
