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Which of the following is equivalent to log_a(b^c)?
Which of the following is equivalent to log_a(b^c)?
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Practice Questions
1 question
Q1
Which of the following is equivalent to log_a(b^c)?
c * log_a(b)
log_a(b) / c
log_a(c) + log_a(b)
log_a(b) - c
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log_a(b^c) = c * log_a(b) by the power rule of logarithms.
Questions & Step-by-step Solutions
1 item
Q
Q: Which of the following is equivalent to log_a(b^c)?
Solution:
log_a(b^c) = c * log_a(b) by the power rule of logarithms.
Steps: 5
Show Steps
Step 1: Identify the expression you want to simplify, which is log_a(b^c).
Step 2: Recall the power rule of logarithms, which states that log_a(x^y) = y * log_a(x).
Step 3: In your expression, b is the base and c is the exponent.
Step 4: Apply the power rule to your expression: log_a(b^c) becomes c * log_a(b).
Step 5: Write down the final simplified expression: log_a(b^c) = c * log_a(b).
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