Question 8
We are to solve
[tex]x^{2.8}=31[/tex]
This can be simplified to
[tex]\begin{gathered} x^{\frac{28}{10}}=31 \\ x^{\frac{14}{5}}=31 \end{gathered}[/tex]
Raising both sides of the equation to a power of 5 we have
[tex]\begin{gathered} x^{\frac{14}{5}\times5}=31^5 \\ x^{14}=31^5 \\ x^{14}=28629151 \end{gathered}[/tex]
By raising both sides of the equation to power of 1/14, we get
[tex]\begin{gathered} x^{14\times\frac{1}{14}}=28629151^{\frac{1}{14}} \\ x=\sqrt[14]{28629151} \end{gathered}[/tex]
Simplifying this we get
[tex]x=3.40901[/tex]
