write the expression as a sum or difference of logarithms. express powers as factors show all work
log4 sqrt pq/7
log sqrt(pq/7)
= log (pq/7)^(1/2)
= 1/2 log(pq/7)
= 1/2 (log p + log q - log 7)
The base doesn't matter. This is just dealing with the properties of logs.
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As the animals left the ark, Noah told them to go forth and multiply. After some while, Noah happened upon two snakes sunning themselves. "Why aren't you multiplying?" Noah asked. The snakes replied, "We can't, we're adders."
So Noah sent the snakes into the forest and told them to try again. Soon he returned and saw many little snakes crawling about. He inquired how it was possible, and they snakes replied, "We found we could multiply if we used logs."
To express the expression log₄ √(pq/7) as a sum or difference of logarithms, we will use the properties of logarithms.
1. Start by applying the Power Rule of logarithms, which states that logₐ (m^n) = n * logₐ (m).
Applying the Power Rule to our expression, we have:
log₄ √(pq/7) = 1/2 * log₄ (pq/7)
2. Next, use the Quotient Rule of logarithms, which states that logₐ (m/n) = logₐ (m) - logₐ (n).
Transform the expression further using the Quotient Rule:
1/2 * log₄ (pq/7) = 1/2 * (log₄ (p) + log₄ (q) - log₄ (7))
3. Finally, rearrange the terms to write the expression as a sum of logarithms:
1/2 * (log₄ (p) + log₄ (q) - log₄ (7))
= 1/2 * log₄ (p) + 1/2 * log₄ (q) - 1/2 * log₄ (7)
Thus, log₄ √(pq/7) can be expressed as the sum of 1/2 * log₄ (p), 1/2 * log₄ (q), and -1/2 * log₄ (7).