Question

Solve the following exponential equation. Express your answer as both an exact expression and a decimal approximation rounded to two decimal places. Use P=2.71828182845905.e^2x-1= 12^x/2

Answer 1

The value of x is 1.12

Step-by-step explanation

Given equation

`\text{ }e^{2x\text{ - 1}}=\text{ 12}^{(x)/(12)}`

The first step is to take the natural logarithms of both sides

`\begin{gathered} \ln(e^{2x\text{ - 1}})\text{ = }\ln(12^{(x)/(12)}) \\ \end{gathered}`

Solve for x

`\begin{gathered} 2x\text{ - 1 =}(x)/(12)\ln12 \\ 2x\text{ - 1= }(x)/(2) \\ 2x\text{ - 1 = }(x)/(12)*2.484906649 \\ \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{ }(4x)/(4)\text{ = }(4.484906649)/(4) \\ \text{ x =1.12} \end{gathered}`

Hence, the value of x is 1.12