Lg(x^2-5x+68)=2(lg16-lg2)

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вопрос

First, simplify the left side of the equation by using the properties of logarithms:

lg(x^2-5x+68) = lg(16) - lg(2)^2

Now, use the properties of logarithms to simplify even further:

lg(x^2-5x+68) = lg(16) - 2

Since lg(16)=lg(2^4)=4, the equation becomes:

lg(x^2-5x+68) = 4 - 2
lg(x^2-5x+68) = 2

Now, rewrite the equation without the logarithms:

x^2 - 5x + 68 = 10

Now, move all the terms to one side of the equation:

x^2 - 5x + 58 = 0

This is a quadratic equation. To solve it, you can either factor it or use the quadratic formula:

x^2 - 5x + 58 = 0

The equation does not factor easily, so it's best to use the quadratic formula:

x = [-(-5) ± √((-5)^2 - 4158)] / 2*1

x = [5 ± √(25 - 232)] / 2
x = [5 ± √(-207)] / 2
x = [5 ± √(207)i] / 2

Therefore, the solutions are:

x = (5 + √207i) / 2 or x = (5 - √207i) / 2