Question

Solve question: 3^(2x-4) = 31

Answer 1

We want to solve

`3^(2x-4)=31`
`\begin{gathered} 3^(2x-4)=31 \\ \\ Taking\text{ the natural logarithm of both sides} \\ \\ ln(3^(2x-4))=ln(31) \\ \\ (2x-4)ln(3)=ln(31) \\ \\ (2x-4)=(ln(31))/(ln(3)) \\ \\ 2x=(ln(31))/(ln(3))+4 \\ \\ x=(ln(31))/(2ln(3))+2 \\ \\ x=3.562874929 \\ \\ x=3.563\text{ \lparen to three decimal places\rparen} \end{gathered}`