To answer this question we have to use logarithms.
Apply the natural logarithm to both sides of the equation:
[tex]\begin{gathered} 7^x=77 \\ ln7^x=ln77 \end{gathered}[/tex]
Apply the property of exponents in logarithms:
[tex]\begin{gathered} xln7=ln77 \\ \end{gathered}[/tex]
Solve for x:
[tex]\begin{gathered} x=\frac{ln77}{ln7} \\ x=2.23 \end{gathered}[/tex]
It means that the correct answer is D. x=2.23.
