What is 3log2 x-(log2 3-log2(x+4)) written as a single logarithm?

Mathematics

2 answers:

Art [367]3 years ago

5 0

Answer:

the answer is c on edge

Step-by-step explanation:

it's the closest one so

log2 (x^3/3)/x+4

which is c

zloy xaker [14]3 years ago

3 0

Answer:
log₂( $\frac{x^2(x+4)}{3}$ )

Explanation:
Before we begin, remember the following:
logₐ(x) - logₐ(y) = logₐ( $\frac{x}{y}$ )
alog(x) = log(xᵃ)

Now, for the given we have:
3 log₂(x) - (log₂3 - log₂(x+4))
log₂(x²) - log₂( $\frac{3}{x+4}$ )

log₂( $\frac{x^2}{ \frac{3}{x+4} }$ ) = log₂( $\frac{x^2(x+4)}{3}$ )

Hope this helps :)

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PLSS ANSWER MY QUESTION

Taya2010 [7]

Answer:

1) Area of frame: $140cm^2$ ; Area of picture: $40cm^2$ ; Total Area: $180cm^2$ .

2) Area 1 = $48cm^2$ ; Area 2 = $12cm^2$ ; total area = $60cm^2$ [first answer line : $60cm^2$ ]

Step-by-step explanation:

1. So to answer this question, you have to find the inner photo area first (which you will then subtract from the overall rectangle area to get the photo frame area).

To find area, you multiply length x width. For this question, there are not enough measurements given to initially multiply length and width. So, assuming that the photo is centered on the frame and the frame width is consistent along all sides, you find the difference between the overall length (12) and the picture length (5).

12 - 5 = 7

The leftover area (outside of the picture) is 7 cm (half of seven on both sides), so one side can be assumed to be : 3.5 cm

this means that 15 cm - 3.5 cm of both sides lengths (difference between the two lengths given) is the height of the photo, 15 - 3.5(2) = 8

So, the dimensions/measurements of the photo are 5 cm by 8 cm.

This means that the inner photo area is 40 (5 x 8) cm

The area of the frame will be the area of the total rectangle [12 x 15] - the inner photo area [40]. [ (12)(15) - 40 ]

[180 - 40] = 140 cm

(area is measured in squared units, so the area of the frame should be written as $140cm^{2}$ ; and the area of the photo should be written as $40cm^{2}$ )

The total area is the entire area of the rectangle: (12)(15) = 180. (This should be written as $180cm^2$ )

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2) Finding the area of a shape that isn't a simple rectangle is easier if you separate the shape into smaller rectangles. I will separate the two rectangles into 4 x 12 and 2 x 6 [6 cm would be the remaining side length if you remove the length of 4].

{you can separate the shape in multiple ways, so my answer is only one answer to this problem out of other splits.}

as mentioned, the area is length x width.

4 x 12 = 48.

2 x 6 = 12. Once again, you should write area in squared units.

(the area 1 should be written as $48cm^{2}$ ; the area 2 should be written as $12cm^2$ )