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aliya0001 [1]
1 year ago
8

Log(x⁴+3x³) - log(X + 3 ) + log2 - log6 = 2logx . find the value of x

Mathematics
1 answer:
AfilCa [17]1 year ago
7 0

The given equation is

\begin{gathered} \log (x^4+3x^3)-\log (x+3)+\log 2-\log 6=2\log x \\ \log (\frac{x^4+3x^{3^{}}}{x+3})+\log \frac{2}{6}=\log x^2 \\ \log \frac{x^3(x+3)}{x+3}+\log \frac{1}{3}=\log x^2 \\ \log x^3+\log \frac{1}{3}=\log x^2 \\ \log \frac{x^3}{3}=\log x^2 \\ \frac{x^3}{3}=x^2 \\ x^3-3x^2=0 \\ x^2(x-3)=0 \end{gathered}

hence

x=0\text{ or x=3}

But x cannot be zero so x=3

So the value of x is 3

h

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Michael has to pay $300 rent. He gets paid $18 per hour. Write an equation that represents his profit, y, after working x hours.
mixer [17]

Answer:

A.) 300 = $18x

B.) 277.50 = $9.25x

C.) 360 years

Step-by-step explanation:

5 0
3 years ago
Find the midpoint of the segment with the following endpoints.<br> (-8,7) and (0,1)
Mamont248 [21]
(-8 + 0 / 2) (7 + 1 / 2)
(-8/2) (8/2)
(-4) (4)
Midpoint = (-4,4) [Answer]
6 0
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Math question down below
Alja [10]

Answer:

E

E is the only one that ends with 70 and is also all multiples of 6.

4 0
3 years ago
I dont get it plzzz help me
cricket20 [7]

Given Equation: \frac{1}{3}h-4(\frac{2}{3}h-3)=\frac{2}{3}h-6

Let us remove parenthesis first.

In order to remove parenthesis, we need to distribute -4 over parenthesis (2/3 h -3).

Distributing -4 over (2/3 h -3), we get,

-4*2/3 h - 4*-3 = -8/3 h + 12.

Substituting this value in original equation, we get

\frac{1}{3}h-\frac{8}{3}h+12 =\frac{2}{3}h-6

Now, in order to make the equation easy to solve, we always remove fractions. In order to remove fraction, we need to find the lowest common denominator of all terms(lcd).

The fraction terms has 3 in denominators, so we could multiply each and every term by 3 to remove 3's from denominators.

Multiplying each equation by 3, we get,

3*\frac{1}{3}h-3*\frac{8}{3}h+3*12 =3*\frac{2}{3}h-3*6

On simplfying this step, we get

1h -8h+36=2h-18

Combining like terms on left side, we get

-7h +36 = 2h -18.

Subtracting 36 from both sides, we get

-7h +36 -36= 2h -18-36.

-7h=2h-54

Subtracting 2h from both sides, we get

-7h-2h=2h-54-2h

-9h = -54

Dividing both sides by -9.

-9h/-9 = -54/-9

h = 6.

Therefore, final answer is h=6.


5 0
3 years ago
Michelle ordered 200 T-shirts to sell at the school carnival. She paid $2.80 per shirt, plus 5% of the total order for shipping.
djyliett [7]

Answer: She should sell each T-Shirt for at least $4.41

Step-by-step explanation:

First you need to figure out what the total cost of the 200 t shirts was plus shipping. so 200 t shirts for 2.8 would cost $560 + a 5% shipping fee ($28) = 588 if she wants to markup by 150. you would then multiply 588 * 1.5 = $882. This would be the final money she wants to make by the end of her school carnival. Divide 882/200 (amnt of t-shirts) to get $4.41 per shirt

4 0
2 years ago
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