The equation given is
[tex]2^{\left\{3x\right\}}=91[/tex]
Evaluate for x
[tex]\begin{gathered} Apply\text{ exponent rules} \\ 3x\ln \left(2\right)=\ln \left(91\right) \\ x=\frac{\ln\left(91\right)}{3\ln\left(2\right)}=2.16926\approx2.17 \end{gathered}[/tex]
Hence, Option D is the correct answer.
