Answered

Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Discover comprehensive solutions to your questions from a wide network of experts on our user-friendly platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

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

Solve The Following Exponential Equation Express Your Answer As Both An Exact Expression And A Decimal Approximation Rounded To Two Decimal Places Use P27182818 class=

Sagot :

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

Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. We hope this was helpful. Please come back whenever you need more information or answers to your queries. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.