Question

2^(2x)-15×11^(x)=11^(x)-15×2^(2x+3)​

Answer 1

Ответ:

х=2

Свойства степени.

Answer 2

To solve the equation 2^(2x) - 15 * 11^(x) = 11^(x) - 15 * 2^(2x + 3), we can start by simplifying the equation. Let's break it down step by step:

1. Distribute the exponents using the exponent rule a^(b + c) = a^b * a^c: 2^(2x) - 15 * 11^(x) = 11^(x) - 15 * 2^(2x) * 2^3

2. Simplify further by combining like terms: 2^(2x) - 15 * 11^(x) = 11^(x) - 15 * 8 * 2^(2x)

3. Rearrange the equation to isolate the terms with the same base, 2^(2x): 2^(2x) - 11^(x) = 15 * 8 * 2^(2x) - 15 * 11^(x)

4. Combine the terms on both sides of the equation: -11^(x) = 15 * 8 * 2^(2x) - 15 * 11^(x) - 2^(2x)

5. Simplify the equation further: -11^(x) = 120 * 2^(2x) - 15 * 11^(x) - 2^(2x)

6. Group the terms involving 2^(2x): -11^(x) + 15 * 11^(x) = 120 * 2^(2x) - 2^(2x)

7. Simplify the equation again: 4 * 11^(x) = 118 * 2^(2x)

Now, the equation has been simplified to 4 * 11^(x) = 118 * 2^(2x). At this point, it is not possible to solve this equation algebraically, as it involves two different exponential terms that cannot be easily manipulated. To find an approximate solution, numerical methods or calculators can be used.