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Sunny_sXe [5.5K]
4 years ago
7

What equation this show The cost of 10 pounds of potatoes is 8 dollars

Mathematics
1 answer:
Alekssandra [29.7K]4 years ago
8 0
To formulate the equation that shows the cost of 10 pounds of potatoes is 8 dollars we proceed as follows;
suppose the cost 1 pound is x;
thus,
total cost=(amount in pounds)*(price of one pound)
total cost=$8
amount=10 pounds
cost of one pound=x
thus the equation is;
8=10x
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In the equation

3^x = 3\cdot 2^x

divide both sides by 2^x to get

\dfrac{3^x}{2^x} = 3 \cdot \dfrac{2^x}{2^x} \\\\ \implies \left(\dfrac32\right)^x = 3

Take the base-3/2 logarithm of both sides:

\log_{3/2}\left(\dfrac32\right)^x = \log_{3/2}(3) \\\\ \implies x \log_{3/2}\left(\dfrac 32\right) = \log_{3/2}(3) \\\\ \implies \boxed{x = \log_{3/2}(3)}

Alternatively, you can divide both sides by 3^x:

\dfrac{3^x}{3^x} = \dfrac{3\cdot 2^x}{3^x} \\\\ \implies 1 = 3 \cdot\left(\dfrac23\right)^x \\\\ \implies \left(\dfrac23\right)^x = \dfrac13

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(Both answers are equivalent)

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