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pychu [463]
3 years ago
11

3. Solve 2log4y - log4 (5y - 12) = 1/2​

Mathematics
1 answer:
Ilia_Sergeevich [38]3 years ago
4 0

Answer:

y =  4  or y = 6

Step-by-step explanation:

2log4y - log4 (5y - 12) = 1/2

​2log_4(y) - log_4(5y-12) = log_4(2)           apply law of logarithms

log_4(y^2) + log_4(1/(5y-12)) = log_4(/2)    apply law of logarithms

log_4(y^2/(5y-12)) = log_4(2)                     remove logarithm

y^2/(5y-12) = 2                                            cross multiply

y^2 = 10y-24                                                  rearrange and factor

y^2 - 10y + 24 = 0

(y-4)(y-6) = 0

y= 4 or y=6

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The equation indicates that the center of the window is 12 feet from the ground and the distance the window spans 6 feet.

<h3>What is the general equation of a circle?</h3>

The equation of a circle is given by the formula,

(x-a)^{2} + (y -b)^{2} = r^{2}

where (a,b) is the coordinate of the center of the circle, and r is the radius of the circle.

According to the given equation, if we compare this equation with the general equation of the circle.

(x-4)^{2} + (y-12)^{2} = 9

(x-a)^{2} + (y -b)^{2} = r^{2}

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On  observing this equation we will get that the value of (a,b) is (4,12).

Thus, The equation indicates that the center of the window is 12 feet from the ground

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Hence, The equation indicates that the center of the window is 12 feet from the ground and the distance the window spans 6 feet.

To learn more about Equation of the circle from the given link

brainly.com/question/22223658

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