Question

find log(x^2-6x-6)=0​

Answer 1

Answer:

x=3 and X=2

Step-by-step explanation:

${x}^{2} - 6x + 6 = 0 \\ {x}^{2} - 3x - 2x + 6 = 0 \\ ( {x}^{2} - 3x) + ( - 2x + 6) = 0 \\ x(x - 3) - 2(x - 3) = 0 \\ (x - 3)(x - 2) = 0 \\ x - 3 = 0 \: and \: x - 2 = 0 \\ x = 3 \: and \: x = 2 \: answer$

Answer 2

Answer:

The solutions to the equation $log(x^2-6x-6) = 0$ are

$x = 3 + \sqrt{15} \ or \ x = 3 - \sqrt{15}$

Step-by-step explanation:

To solve the equation:

$log(x^2-6x-6) = 0$

We first need to use the definition of logarithms:

$log(b, a) = c$ is equivalent to $b^c = a$

Using this definition, we can rewrite the equation as:

$x^2 - 6x - 6 = 10^0$

Simplifying the right-hand side, we get:

$x^2 - 6x - 6 = 1$

Now we can move all the terms to one side of the equation:

$x^2 - 6x - 7 = 0$

To solve this quadratic equation, we can use the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = -6, and c = -7. Substituting these values, we get:

x = [6 ± sqrt((-6)^2 - 4(1)(-7))] / 2(1)

Simplifying under the square root:

x = [6 ± sqrt(60)] / 2

x = 3 ± sqrt(15)

Therefore, the solutions to the equation $log(x^2-6x-6) = 0$ are:

$x = 3 + \sqrt{15} \ or \ x = 3 - \sqrt{15}$

To learn more about logarithm: https://brainly.in/question/3486338

To learn more about quadratic equations:  https://brainly.in/question/5074153

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