Question

4 в степени х минус 3 в степени х равно 1 найти х, только не подбором

Answer 1

4х-3х=1
1х=1
Х=1:1
Х=1
ответ: х=1

Answer 2

Problem Analysis

We are given the equation 4^x - 3^x = 1 and we need to find the value of x without using trial and error.

Solution

To solve the equation 4^x - 3^x = 1, we can rewrite it as (2^2)^x - (3^1)^x = 1. Simplifying further, we get 2^(2x) - 3^x = 1.

Let's solve this equation step by step:

1. Let's substitute y = 2^x. The equation becomes y^2 - 3^x = 1. 2. Rearranging the equation, we get y^2 = 1 + 3^x. 3. Taking the square root of both sides, we get y = sqrt(1 + 3^x). 4. Substituting back y = 2^x, we get 2^x = sqrt(1 + 3^x). 5. Squaring both sides, we get 2^(2x) = 1 + 3^x.

Now, we have a new equation 2^(2x) = 1 + 3^x. Let's solve this equation:

1. Subtracting 3^x from both sides, we get 2^(2x) - 3^x = 1.

Therefore, the equation 4^x - 3^x = 1 is equivalent to the equation 2^(2x) - 3^x = 1.

Unfortunately, I couldn't find a direct algebraic method to solve this equation without using trial and error or numerical methods. The equation involves exponential terms, and finding an exact solution may not be possible.

If you have any further questions, please, let me know.

Answer 3

Task: Solve the equation 4^x - 3^x = 1 for x without using trial and error.

To solve the equation 4^x - 3^x = 1 without using trial and error, we can use algebraic methods. Let's go step by step:

1. Rewrite the equation: 4^x - 3^x = 1 2. Notice that both terms have the same base, which is a common factor. We can rewrite the equation as follows: (2^2)^x - (3^1)^x = 1 3. Apply the exponent rule for the first term: 2^(2x) - 3^x = 1 4. Now we have two terms with the same base, so we can combine them into a single term: 2^(2x) - 2^(3x/2) = 1 5. Apply the exponent rule again to combine the terms: 2^(2x - 3x/2) = 1 6. Simplify the exponent: 2^(4x/2 - 3x/2) = 1 7. Combine the terms in the exponent: 2^(x/2) = 1 8. Since 2^0 = 1, we can equate the exponent to 0: x/2 = 0 9. Solve for x: x = 0 * 2 = 0

Therefore, the solution to the equation 4^x - 3^x = 1 without using trial and error is x = 0.

Note: This solution is based on algebraic methods and does not involve trial and error.