datboulreese4048
20.05.2021 •
Mathematics
Brand A green beans costs $7.00 for a 16 ounce pack and Brand B green beans costs $9.00 for a 20 ounce pack
a. Which brand of green beans has the lowest price per ounce?
b. Explain your reasoning. Be specific (include the price per ounce for each brand in your explanation),
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Ответ:
Explanation:
Before we begin, remember that:
log (x) + log (y) = log (xy)
log x² = 2 log x
log₄ (4) = 1
Now, let's see the question we have:
For the left hand side:
log₄ x + log₄ (x+6) = log₄ x(x+6)
For the right hand side:
2 can be rewritten as:
log₄ (4)²
Now, equating the left hand side with the right hand side:
log₄ x(x+6) = log₄ (4)²
We can deduce that:
x (x+6) = (4)²
We will now solve for x as follows:
x (x+6) = (4)²
x² + 6x = 16
x² + 6x - 16 = 0
(x-2)(x+8) = 0
either x-2 = 0 > x=2
or x+8 = 0 > x = -8
Note: The negative solution is usually rejected as no log can hold a negative value. However, since it is not eliminated in the given choices, we will consider it as a potential solution
Hope this helps :)