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3 years ago

choose the single logarithm expression that is equivalent to the one shown 1 / 3 log 3x + 2 / 3 log 3x

Mathematics

1 answer:

alexgriva [62]3 years ago

6 0

Answer:

$\log (3x)$

Step-by-step explanation:

The given logarithmic expression is:

$\frac{1}{3}\log(3x)+ \frac{2}{3}\log(3x)$

This is the same as:

$\frac{1}{3}\log(3x)+ \frac{1}{3}\log(3x)^2$

$\frac{1}{3}(\log(3x)+ \log(3x)^2)$

We now apply the product rule to get:

$\frac{1}{3}\log(3x)\times (3x)^2$

$\frac{1}{3}\log (3x)^3$

We now apply the power rule to get;

$\frac{3}{3}\log (3x)=\log (3x)$

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Step-by-step explanation:

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The corners of a meadow are shown on a coordinate grid. Ethan wants to fence the meadow. What length of fencing is required?

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Answer:

34.6 units

Step-by-step explanation:

The lenght of fencing required is the total distance between point A to B, B to C, C to D, and D to A. That is the distance between all 4 corners of the meadow.

The coordinates of the corners of the meadow is shown on a coordinate plane in the attachment. (See attachment below).

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Distance between B(2, 6) and C(7, 1):

$BC = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Let,

$B(2, 6) = (x_1, y_1)$

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Distance between C(7, 1) and D(3, -5):

$CD = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Let,

$C(7, 1) = (x_1, y_1)$

$D(3, -5) = (x_2, y_2)$

$CD = \sqrt{(3 - 7)^2 + (-5 - 1)^2}$

$CD = \sqrt{(-4)^2 + (-6)^2}$

$CD = \sqrt{16 + 36} = \sqrt{52}$

$CD = 7.2$ (nearest tenth)

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$DA = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Let,

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Answer:

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Step-by-step explanation:

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