[tex]\begin{gathered} 2^{4x}=78,\text{ applying natural logarithm to both sides} \\ \ln (2^{4x})=\ln (78) \\ 4x\ln (2)=\ln (78) \\ 4x=\frac{\ln(78)}{\ln(2)} \\ \\ x=\frac{\ln(78)}{4\ln(2)} \\ \\ x=1.5713505547155620854626378995511278105970627023708796074985540450 \\ \\ x\approx1.57 \end{gathered}[/tex]
the answer is 1.57
