Question

2*4^х-7*10^х+5*25^х=0

Answer 1

Ответ:

Объяснение:

2·4ˣ⁻⁷·10ˣ⁺⁵·25ˣ=0

2·(2²)ˣ⁻⁷·(2·5)ˣ⁺⁵·(5²)ˣ=0

2·2²ˣ⁻¹⁴·2ˣ⁺⁵·5ˣ⁺⁵·5²ˣ=0

2¹⁺²ˣ⁻¹⁴⁺ˣ⁺⁵·5ˣ⁺⁵⁺²ˣ=0

2³ˣ⁻⁸·5³ˣ⁺⁵=0⇒уравнение не имеет решений.

Answer 2

To solve the equation 2 * 4^x - 7 * 10^x + 5 * 25^x = 0, we can simplify it by expressing the powers of numbers in terms of a common base. In this case, we'll use 2 as the common base.

Let's rewrite the equation using the common base of 2:

2 * (2^2)^x - 7 * (2 * 5)^x + 5 * (5^2)^x = 0

Simplifying further:

2 * 2^(2x) - 7 * 2^x * 5^x + 5 * 5^(2x) = 0

Now, let's rewrite the equation using exponential notation:

2^(2x + 1) - 7 * 2^x * 5^x + 5^(2x + 1) = 0

To solve this equation, we need to use numerical methods or graphing calculators because it involves exponential terms with different bases. It does not have a simple algebraic solution.

If you provide a specific range or constraints for the variable x, I can attempt to find an approximate solution using numerical methods.