Log x + log (x - 6) =3

x = 3 + sqrt(e^3 + 9)

Step-by-step explanation:

Solve for x over the real numbers:

log(x) + log(x - 6) = 3

Hint: | Combine logarithms.

log(x - 6) + log(x) = log(x (x - 6)):

log(x (x - 6)) = 3

Hint: | Eliminate the logarithm from the left hand side.

Cancel logarithms by taking exp of both sides:

x (x - 6) = e^3

Hint: | Write the quadratic polynomial on the left hand side in standard form.

Expand out terms of the left hand side:

x^2 - 6 x = e^3

Hint: | Take one half of the coefficient of x and square it, then add it to both sides.

Add 9 to both sides:

x^2 - 6 x + 9 = e^3 + 9

Hint: | Factor the left hand side.

Write the left hand side as a square:

(x - 3)^2 = e^3 + 9

Hint: | Eliminate the exponent on the left hand side.

Take the square root of both sides:

x - 3 = sqrt(e^3 + 9) or x - 3 = -sqrt(e^3 + 9)

Hint: | Look at the first equation: Solve for x.

Add 3 to both sides:

x = 3 + sqrt(e^3 + 9) or x - 3 = -sqrt(e^3 + 9)

Hint: | Look at the second equation: Solve for x.

Add 3 to both sides:

x = 3 + sqrt(e^3 + 9) or x = 3 - sqrt(e^3 + 9)

Hint: | Now test that these solutions are correct by substituting into the original equation.

Check the solution x = 3 - sqrt(e^3 + 9).

log(x) + log(x - 6) ⇒ log((3 - sqrt(e^3 + 9)) - 6) + log(3 - sqrt(e^3 + 9)) = 2 i π + 3 ≈ 3 + 6.28319 i:

So this solution is incorrect

Hint: | Check the solution x = 3 + sqrt(e^3 + 9).

log(x) + log(x - 6) ⇒ log(3 + sqrt(e^3 + 9)) + log((3 + sqrt(e^3 + 9)) - 6) = 3:

So this solution is correct

Hint: | Gather any correct solutions.

The solution is:

x = 3 + sqrt(e^3 + 9)

9514 1404 393

  x = 3 + √1009 ≈ 34.765

Step-by-step explanation:

Take the antilog and solve the resulting quadratic.

  x(x -6) = 10^3

  x^2 -6x +9 = 1009 . . . . . . add (-6/2)^2 to complete the square

  (x -3)^2 = 1009 . . . . . . . . . write as a square

  x = 3 + √1009 ≈ 34.765 . . . . . square root and add 3

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Only the positive root makes any sense, since the log of a negative number is not defined (in real numbers).

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For the graph, we subtracted 3 so we are looking for the x-intercept where f(x)=0.

4th option is correct xy=-10

if this was to u plzz mark me the brainliest

step-by-step explanation:

if you want to solve percent error follow these steps.

1. subtract the accepted value from the experimental value.

2. take the absolute value of step 1.

3. divide that answer by the accepted value.

4. multiply that answer by 100 and add the % symbol to express the answer as a percentage.

if you want to solve percent of change just do this.

1. work out the difference (increase) between the two numbers you are comparing.

2. divide the increase by the original number and multiply the answer by 100. if your answer is a negative number then this is a percentage decrease.

hope this : )