Log(x^2-3x-10)=3 решение

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To solve the equation log(x^2 - 3x - 10) = 3, we first need to convert the logarithmic equation into an exponential form.

The logarithmic equation log(x^2 - 3x - 10) = 3 can be rewritten as:

x^2 - 3x - 10 = 10^3

x^2 - 3x - 10 = 1000

Next, we need to solve the quadratic equation x^2 - 3x - 10 = 1000 by moving all terms to one side:

x^2 - 3x - 10 - 1000 = 0

x^2 - 3x - 1010 = 0

Now, we can solve this quadratic equation using the quadratic formula:

x = (-(-3) ± √((-3)^2 - 41(-1010))) / (2*1)

x = (3 ± √(9 + 4040)) / 2

x = (3 ± √4049) / 2

x = (3 ± 63.62) / 2

x1 ≈ (3 + 63.62) / 2 ≈ 33.81

x2 ≈ (3 - 63.62) / 2 ≈ -30.81

Therefore, the solutions to the equation log(x^2 - 3x - 10) = 3 are approximately x = 33.81 and x = -30.81.