a)
[tex]e^{\ln (\sqrt[]{5})}[/tex]
Simplify
[tex]\ln (\sqrt[]{5})=\frac{1}{2}\ln (5)[/tex]
So, we have
[tex]e^{\frac{1}{2}\ln (5)}[/tex]
Apply the exponent law
[tex]\begin{gathered} (e^{\ln (5)})^{\frac{1}{2}} \\ e^{\ln (5)}=5,\text{ therefore} \\ 5^{\frac{1}{2}}=\sqrt[]{5} \end{gathered}[/tex]
Answer:
[tex]\sqrt[]{5}[/tex]
b)
[tex]e^{\ln (\frac{1}{\pi})}[/tex]
Applying the properties of logarithms
[tex]\begin{gathered} \frac{1}{\pi} \\ \end{gathered}[/tex]
Answer:
[tex]\frac{1}{\pi}[/tex]
c)
[tex]10^{\log (15)}[/tex]
Applying the properties of logarithms
[tex]=15[/tex]
Answer: 15
