Isolve for x: ln(x^2-6x-16)= 0 . help me beacuse I do not have the idea to work it out.

Solve for the value of x: ln(x^2-6x-16)=5. Please help me work it out because I do not have an idea in work it out.

(x^2-6x-15)=e^5

e^5 is approximately 148.41

so x^2-6x=148.41-15

x^2-6x = 133.41

x-6x = sqrt(133.41)

-5x = 11.55

x = 11.55/-5

x = 2.31

unfortunately Sunny made several errors,

Try to sub in x = 2.31, it does not work

form his/hers : (x^2-6x-16)=e^5 ---- Sunny had -15

x^2 - 6x = 148.413 + 16
complete the square by adding 9 to both sides
x^2 - 6x + 9 = 148.413+16+9 = 173.413
(x-3)^2 = 173.413
x-3 = ±√173.413 = ± 13.1686

x = 3 ± 13.1686
x = 16.1686 or x = -10.1686

both work when subbed into the original equation

To solve the equation ln(x^2 - 6x - 16) = 0, follow these steps:

Step 1: Simplify the equation
Since ln(x^2 - 6x - 16) = 0, we can rewrite it using exponentiation. Remember that ln and e are inverse functions, so e^(ln(x)) equals x.
Therefore, e^0 = x^2 - 6x - 16.

Step 2: Remove the exponential form
Since anything raised to the power of 0 is 1, the equation becomes 1 = x^2 - 6x - 16.

Step 3: Rearrange the equation
To solve a quadratic equation, we typically want the equation to be in the form ax^2 + bx + c = 0. Therefore, rearrange the equation to x^2 - 6x - 17 = 0.

Step 4: Solve the quadratic equation
Now that the equation is in standard quadratic form, we can solve for x. There are different methods to do this, such as factoring, completing the square, or using the quadratic formula.
In this case, the equation cannot be easily factored, so we will use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a),

where a = 1, b = -6, and c = -17.

Plugging in these values, we have:
x = (-(-6) ± √((-6)^2 - 4(1)(-17))) / (2(1)).
This simplifies to:
x = (6 ± √(36 + 68)) / 2,
x = (6 ± √104) / 2,
x = (6 ± 2√26) / 2.

Step 5: Simplify the solution
Divide the numerator and denominator of (6 ± 2√26) / 2 by 2 to simplify the expression:
x = 3 ± √26.

Therefore, the solutions to the equation ln(x^2 - 6x - 16) = 0 are x = 3 + √26 and x = 3 - √26.