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torisob [31]
3 years ago
15

Use the properties of logarithms to rewrite each expression in an equivalent form containing a single logarithm.

Mathematics
1 answer:
Scrat [10]3 years ago
6 0

Answer:

\frac{1}{2}\log(16) + \log(3) + \log(\frac{1}{4}) = log(3)

Step-by-step explanation:

Given equation:

\frac{1}{2}\log(16) + \log(3) + \log(\frac{1}{4})

now,

we know the properties of log function as:

1) log(A) + log(B) = log(AB)

2) log(A) - log(B) = \log(\frac{A}{B})

3) log(Aᵇ) = b × log(A)

therefore,

using property 3 we get

\log(16)^{\frac{1}{2}} + \log(3) + \log(\frac{1}{4})

or

\log(4) + \log(3) + \log(\frac{1}{4})

now,

using the property 2 we get

⇒ log(4) + log(3) + log(1) - log(4)

or

⇒ log(3) + log(1)

now,

using the property 1, we get

⇒ log(3 × 1)

or

⇒ log(3)

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then multiply 9 by both sides

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then simplify

y = -18

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Step-by-step explanation:

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2 years ago
What is the equation of the line that passes through the point (-6,-6)and has a slope of -\frac{1}{3}− ?
Gnesinka [82]

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Answer:

  y +6 = (-1/3)(x +6)

Step-by-step explanation:

Given a point and a slope, it is appropriate to use the point-slope form to represent the equation:

  y -k = m(x -h) . . . . . line with slope m through point (h, k)

For your point and slope, the equation is ...

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  y +6 = -1/3(x +6)

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Of course, this can be rearranged to whatever form you need.

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3 0
3 years ago
Please help me with this.
zheka24 [161]

The sin A is equal to 12/13 and the tan (A) is equal to 12/5.

<h3>RIGHT TRIANGLE</h3>

A triangle is classified as a right triangle when it presents one of your angles equal to 90º.  The greatest side of a right triangle is called hypotenuse. And, the other two sides are called cathetus or legs.

The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.

The Pythagorean Theorem says: hypotenuse^2=(leg_1)^2+(leg_2)^2. And the main trigonometric ratios are:

sin(\beta )= \frac{opposite\;leg}{hypotenuse} \\ \\ cos(\beta )= \frac{adjacent\;leg}{hypotenuse} \\ \\ tan(\beta )= \frac{opposite\;leg}{adjacent\;leg} \\ \\

The question gives cos (A)=5/13. If cos (A) is represented by the quotient between the adjacent leg and the hypotenuse, you have:

adjacent leg=5

hypotenuse=13

Therefore, you can find the opposite leg of A from Pythagorean Theorem, see below.

hypotenuse^2=(leg_1)^2+(leg_2)^2\\ \\ 13^2=5^2+(leg_2)^2\\ \\ 169=25+(leg_2)^2\\ \\ 144=(leg_2)^2\\ \\ leg_2=12

Thus, the opposite leg is equal to 12. Now, you can find sin (A) since:

sin(A)= \frac{opposite\;leg}{hypotenuse}=\frac{12}{13}

Finally, you can find the tan (A) since:

tan(a )= \frac{opposite\;leg}{adjacent\;leg}=\frac{12}{5}

Learn more about trigonometric ratios here:

brainly.com/question/11967894

#SPJ1

7 0
2 years ago
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