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If log_a(5) = p and log_a(25) = q, then what is the relationship between p and q
If log_a(5) = p and log_a(25) = q, then what is the relationship between p and q?
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Practice Questions
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Q1
If log_a(5) = p and log_a(25) = q, then what is the relationship between p and q?
q = 2p
q = p/2
q = p^2
q = p + 1
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log_a(25) = log_a(5^2) = 2 log_a(5) = 2p, hence q = 2p.
Questions & Step-by-step Solutions
1 item
Q
Q: If log_a(5) = p and log_a(25) = q, then what is the relationship between p and q?
Solution:
log_a(25) = log_a(5^2) = 2 log_a(5) = 2p, hence q = 2p.
Steps: 6
Show Steps
Step 1: Understand that log_a(5) = p means that 'a' raised to the power of 'p' equals 5.
Step 2: Recognize that log_a(25) can be rewritten because 25 is the same as 5 squared (5^2).
Step 3: Use the property of logarithms that states log_a(b^c) = c * log_a(b).
Step 4: Apply this property to log_a(25): log_a(25) = log_a(5^2) = 2 * log_a(5).
Step 5: Substitute log_a(5) with p: log_a(25) = 2 * p.
Step 6: Since we defined log_a(25) as q, we can say q = 2p.
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