Question

Find the solution of the exponential equation, correct to four decimal places. e²ˣ⁺¹ = 200

Answer 1

To find the solution of the exponential equation e²ˣ⁺¹ = 200, take the natural logarithm of both sides to eliminate the exponential, simplify, and solve for x using a calculator.

Step-by-step explanation:

To find the solution of the exponential equation e²ˣ⁺¹ = 200, we need to isolate the exponent x. Here are the steps:

1. Take the natural logarithm (ln) of both sides of the equation to eliminate the exponential.
2. We have ln(e²ˣ⁺¹) = ln(200).
3. Use the property of logarithms to simplify the left side: (2x + 1)ln(e) = ln(200).
4. Since ln(e) = 1, we have 2x + 1 = ln(200).
5. Subtract 1 from both sides to get rid of the constant term: 2x = ln(200) - 1.
6. Divide both sides by 2 to solve for x: x = (ln(200) - 1) / 2.
7. Using a calculator, plug in the value of ln(200) and calculate x to four decimal places.

The solution to the equation e²ˣ⁺¹ = 200, correct to four decimal places, is x ≈ 1.1182.