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3 years ago

10

10

1 answer:

wlad13 [49]3 years ago

3 0

Not sure but could be C

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What are the roots of the function f(x) = (log(3x ) − 2 log(3)) · (x 2 − 1) with x ∈ R?

slavikrds [6]

$\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}$

Given:

▪ $\sf{f(x) = ( log(3x) - 2log(3))( {x}^{2} - 1) }$ $\ \sf{x \in R}$

Solve:

$\longrightarrow \sf{f(x) = (log(3x) - 2log(3))( {x}^{2} - 1) = 0}$

$\small\longrightarrow \sf{ log(3x) - 2 log(3) = 0 \: \: or \: {x}^{2} - 1 = 0 }$

$\small\longrightarrow \sf{ log(3x) - 2 log(3) = 0}$

$\small\longrightarrow \sf{ log(3x) - 2 log(3) = 0}$

$\small\longrightarrow \sf{ log(3x) - log( {3}^{2} ) = 0}$

$\small\longrightarrow \sf{log_{10}( \dfrac{3x}{9} ) = 0}$

$\small\sf{ \Longrightarrow \dfrac{3x}{9} = {10}^{0} }$

$\small\longrightarrow \sf{ \dfrac{x}{3} = 1}$

$\small \sf{x= \underline{3}}$

Next $\downarrow$

$\small\longrightarrow \sf{{x}^{2} - 1 = 0}$

$\small\longrightarrow \sf{ {x}^{2} = 1}$

$\small\longrightarrow \sf{x = \pm \sqrt{1} }$

$\small\sf{x= (\underline{1},-1)}$

$\small\longrightarrow \sf{ log(3x) = log(3( - 1)) \cancel{ \in}R}$

$\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}$

$\small\bm{The \: \: roots \: \: of \: \: f(x) \: are \: 1 \: and \: 3.}$

4 0

2 years ago

What is the value of y?<br><br> 3<br> 4<br> 5<br> 6

Burka [1]

For a rectangle, the two verticle sides should be congruent (of the same length)

2y+4=10

Subtract 4 from both sides
2y=6

Divide both sides by 2
y=3

Final answer: 3

5 0

3 years ago

Read 2 more answers

A farmer ships pears in crates that weigh 4.5 lb each when empty. Each pear weighs 0.25 lb. The total weight of a crate filled w

Ipatiy [6.2K]

Answer:

one-quarter times the number of pears, plus four and one-half is forty-four and one-half

Step-by-step explanation:

The total weight (44.5 lb) will be the sum of the empty weight (4.5 lb) and the number of pears multiplied by the pear's weight. That can be expressed as ...

one-quarter times the number of pears, plus four and one-half is forty-four and one-half

4 0

2 years ago

Which of the following points lies on the line?

Bond [772]

Answer:

C. (3,-3)

Step-by-step explanation:

5x + 3y = 6

5(3) + 3(-3) = 6

15 + (-9) = 6

therefore point lies on the line

8 0

2 years ago

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Ulleksa [173]

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6 0

3 years ago