Which set of numbers is NOT in the solution set of the inequality x

hi, i dont undertand number 20 because i was absent in class today and i rerally need help, i will appraciate with the help, and

Mariulka [41]

Given:

The equation is,

$2\log _3x-\log _3(x-2)=2$

Explanation:

Simplify the equation by using logarthimic property.

$\begin{gathered} 2\log _3x-\log _3(x-2)=2 \\ \log _3x^2-\log _3(x-2)=2_{}\text{ \lbrack{}log(a)-log(b) = log(a/b)\rbrack} \\ \log _3\lbrack\frac{x^2}{x-2}\rbrack=2 \end{gathered}$

Simplify further.

$\begin{gathered} \log _3\lbrack\frac{x^2}{x-2}\rbrack=2 \\ \frac{x^2}{x-2}=3^2 \\ x^2=9(x-2) \\ x^2-9x+18=0 \end{gathered}$

Solve the quadratic equation for x.

$\begin{gathered} x^2-6x-3x+18=0 \\ x(x-6)-3(x-6)=0 \\ (x-6)(x-3)=0 \end{gathered}$

From the above equation (x - 6) = 0 or (x - 3) = 0.

For (x - 6) = 0,

$\begin{gathered} x-6=0 \\ x=6 \end{gathered}$

For (x - 3) = 0,

$\begin{gathered} x-3=0 \\ x=3 \end{gathered}$

The values of x from solving the equations are x = 3 and x = 6.

Substitute the values of x in the equation to check answers are valid or not.

For x = 3,

$\begin{gathered} 2\log _3(3^{})-\log _3(3-2)=2 \\ 2\log _33-\log _31=2 \\ 2\cdot1-0=2 \\ 2=2 \end{gathered}$

Equation satisfy for x = 3. So x = 3 is valid value of x.

For x = 6,

$\begin{gathered} 2\log _36-\log _3(6-2)=2 \\ 2\log _36-\log _34=2 \\ \log _3(6^2)-\log _34=2 \\ \log _3(\frac{36}{4})=2 \\ \log _39=2 \\ \log _3(3^2)=2 \\ 2\log _33=2 \\ 2=2 \end{gathered}$

Equation satifies for x = 6.

Thus values of x for equation are x = 3 and x = 6.

6 0

1 year ago

Please help( I will give brainliest) Thanks

Katen [24]

Answer:

i think it's c.

Step-by-step explanation:

sorry if this is wrong

5 0

3 years ago

The square root of the quotient of a number n and 3 is equal to the square root of 4 less than the number. Which of the followin

Lisa [10]

Answer:

6

Step-by-step explanation: You can set up the equation: $\sqrt{\frac{n}{3} }$ = $\sqrt{n-4}$ You square both sides to cancel out the squares which leaves you with $\frac{n}{3}$ = n - 4. Then you just solve as normal which ends you up with an answer of 6. You can check this by plugging 6 back into the equation and see that you end up with $\sqrt{2}$ on both sides.

4 0

3 years ago

Graph this function: y=5x Click to select points on the graph.

inessss [21]

Answer:

You did not include your graph, therefore I will explain in the step-by-step everything you should need to know.

Step-by-step explanation:

The standard slope formula is y=mx + b, where m = slope (rise/run) and b = the y intercept.

Using this knowledge, we know that this line has a slope of 5, or 5/1, which means that you will go up 5 and 1 to the right. Since there is no + b part, that means b = 0, so the line begins at 0,0. So, using this information, possible points include 0,0, 5,1, 10,2, 15,3, etc.

3 0

3 years ago

1. Simplify 4/2 +72 - 3N2 (1 point) O 2/8 O 8/2 O 86 0 68

viktelen [127]

Step-by-step explanation:

4√2+ 7√2 - 3√2 = (4 + 7 - 3)√2 = 8√2

Topic: Indices and Surds

If you like to venture further, do check out my insta (learntionary) where I regularly post useful math tips! Thank you!

4 0

3 years ago

Which set of numbers is NOT in the solution set of the inequality x < 12