Question

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

Answer 1

Solution

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)=\frac{ln(31)}{ln(3)} \\ \\ 2x=\frac{ln(31)}{ln(3)}+4 \\ \\ x=\frac{ln(31)}{2ln(3)}+2 \\ \\ x=3.562874929 \\ \\ x=3.563\text{ \lparen to three decimal places\rparen} \end{gathered}$