ANSWER
The value of x is 1.12
EXPLANATION
Given equation
[tex]\text{ }e^{2x\text{ - 1}}=\text{ 12}^{\frac{x}{12}}[/tex]The first step is to take the natural logarithms of both sides
[tex]\begin{gathered} \ln(e^{2x\text{ - 1}})\text{ = }\ln(12^{\frac{x}{12}}) \\ \end{gathered}[/tex]Solve for x
[tex]\begin{gathered} 2x\text{ - 1 =}\frac{x}{12}\ln12 \\ 2x\text{ - 1= }\frac{x}{2} \\ 2x\text{ - 1 = }\frac{x}{12}\times2.484906649 \\ \text{ 2x - 1= 2.484906649x/2} \\ \text{ cross multiplt} \\ 2(2x\text{ - 1\rparen = 2.484906649} \\ 4x\text{ - 2 = 2.484906649} \\ \text{ Add 2 to the both sides of the equation} \\ \text{ 4x = 2.484906649 + 2} \\ 4x\text{ = 4.484906649} \\ \text{ Divide both sides by 4} \\ \text{ }\frac{4x}{4}\text{ = }\frac{4.484906649}{4} \\ \text{ x =1.12} \end{gathered}[/tex]Hence, the value of x is 1.12