Question

10^(4x)-133*100^x+1000=0.

Answer 1

Ответ и решение во вложении)

Answer 2

To solve the equation 10^(4x) - 133 * 100^x + 1000 = 0, we can use a substitution to simplify it. Let's substitute y = 10^x.

Now we have the equation y^4 - 133 * (y^2) + 1000 = 0.

Let's solve this quadratic equation by factoring:

(y - 10)(y + 10)(y^2 - 100) = 0.

Now we have three separate equations to solve:

1. y - 10 = 0: y = 10.

2. y + 10 = 0: y = -10.

3. y^2 - 100 = 0: (y - 10)(y + 10) = 0.

   Solving this equation, we get two more solutions: y - 10 = 0: y = 10. y + 10 = 0: y = -10.

Now that we have the values of y, we can substitute them back into the equation y = 10^x:

1. y = 10: 10 = 10^x. Taking the logarithm of both sides: log(10) = log(10^x). 1 = x.

2. y = -10: -10 = 10^x. There is no real solution for this equation since raising 10 to any power will always yield a positive value.

Therefore, the only real solution to the equation 10^(4x) - 133 * 100^x + 1000 = 0 is x = 1.