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If log_a(2) = x and log_a(3) = y, then log_a(6) is equal to?
If log_a(2) = x and log_a(3) = y, then log_a(6) is equal to?
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Practice Questions
1 question
Q1
If log_a(2) = x and log_a(3) = y, then log_a(6) is equal to?
x + y
xy
x - y
x/y
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log_a(6) = log_a(2 * 3) = log_a(2) + log_a(3) = x + y.
Questions & Step-by-step Solutions
1 item
Q
Q: If log_a(2) = x and log_a(3) = y, then log_a(6) is equal to?
Solution:
log_a(6) = log_a(2 * 3) = log_a(2) + log_a(3) = x + y.
Steps: 5
Show Steps
Step 1: Understand that log_a(6) can be rewritten using the property of logarithms that states log_a(m * n) = log_a(m) + log_a(n).
Step 2: Identify that 6 can be expressed as the product of 2 and 3, so we can write log_a(6) as log_a(2 * 3).
Step 3: Apply the property from Step 1: log_a(6) = log_a(2) + log_a(3).
Step 4: Substitute the values given in the question: log_a(2) = x and log_a(3) = y.
Step 5: Therefore, log_a(6) = x + y.
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