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The properties that were used to derive the properties of logarithms are:
1. a^x · a^y = a^(x+y)
2. a^x / a^y = a^(x - y)
3. a^0 = 1
4. a^(-x) = 1 / x
5. (a^x)^y = a^(<span>xy)</span><span>
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Number of pounds of macadamia nuts is 8 pounds and number of pounds of almonds is 4 pounds.
<u>Step-by-step explanation:</u>
Step 1:
Given total pounds of mixture = 12 pounds, cost of macadamia nuts per pound = $9, cost of almonds per pound = $5.25, total cost of mixture per pound = $7.75.
Let number of pounds of macadamia nuts be x and number of pounds of almonds be 12-x.
Step 2:
Form an equation using the above information.
⇒ 9x + 5.25 (12-x) = 12 × 7.75
⇒ 9x + 63 - 5.25x = 93
⇒ 9x - 5.25x = 30
⇒ 3.75x = 30
⇒ x = 8
Number of macadamia nuts is 8 pounds.
Step 3:
Calculate number pounds of almonds
⇒ Number of pounds of almonds = 12 - x = 4 pounds.
