Example Question - exponential equation solution
Here are examples of questions we've helped users solve.
Solving Exponential Equation with Identical Base
문제는 다음과 같이 주어집니다: \(3^{-1-\sqrt5} \times 3^{1+\sqrt5}\) 이 문제를 해결하는 과정은 다음과 같습니다: 우선 지수법칙을 사용하여 같은 밑을 가진 지수의 곱셈을 처리합니다: \(a^m \times a^n = a^{m+n}\) 위의 법칙을 적용합시다: \(3^{-1-\sqrt5} \times 3^{1+\sqrt5} = 3^{(-1-\sqrt5) + (1+\sqrt5)} = 3^{0}\) 어떠한 수를 0으로 거듭제곱하면 항상 1입니다. 즉: \(3^{0} = 1\) 따라서 주어진 식의 값은 1입니다. 선택지를 확인하니 1에 해당하는 선택지는 (3)번입니다. 따라서 올바른 답은 (3) 1입니다.
Solving Exponential Equation
The given equation to solve is: e^(4 - 7x) + 11 = 20 First, isolate the exponential term by subtracting 11 from both sides: e^(4 - 7x) + 11 - 11 = 20 - 11 e^(4 - 7x) = 9 Now, to solve for x, apply the natural logarithm (ln) to both sides, because ln(e^y) = y: ln(e^(4 - 7x)) = ln(9) This simplifies to: 4 - 7x = ln(9) Now, isolate x by subtracting 4 from both sides, and then divide by -7: 4 - 7x - 4 = ln(9) - 4 -7x = ln(9) - 4 x = (ln(9) - 4) / (-7) Using a calculator to find the numerical approximation for ln(9): x ≈ (2.1972 - 4) / (-7) x ≈ (-1.8028) / (-7) x ≈ 0.25754 Therefore, the solution to the equation is approximately x ≈ 0.25754.
Solving Exponential Equation
The equation provided in the image is: \( e^{4x} - 7x + 11 = 20 \) To solve for \( x \), follow these steps: 1. Isolate the exponential term by moving all other terms to the other side of the equation: \( e^{4x} = 20 - 11 \) 2. Simplify the right side: \( e^{4x} = 9 \) 3. Take the natural logarithm of both sides to remove the exponential: \( \ln(e^{4x}) = \ln(9) \) 4. Knowing that \( \ln(e^y) = y \), simplify the left side: \( 4x = \ln(9) \) 5. Finally, solve for \( x \) by dividing both sides by 4: \( x = \frac{\ln(9)}{4} \) Therefore, the solution to the equation is: \( x = \frac{\ln(9)}{4} \)
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com