Which of the following represents the change of base formula for logarithms?

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Question: Which of the following represents the change of base formula for logarithms?

Options:

Correct Answer: log_a(b) = log_c(b) / log_c(a)

Solution:

The change of base formula states that log_a(b) can be expressed as log_c(b) divided by log_c(a).

Which of the following represents the change of base formula for logarithms?

Which of the following represents the change of base formula for logarithms?

Step 1: Understand what a logarithm is. A logarithm log_a(b) answers the question: 'To what power must we raise a to get b?'
Step 2: Identify the base of the logarithm. In log_a(b), 'a' is the base.
Step 3: Recognize that sometimes we want to change the base of the logarithm to a different base 'c'.
Step 4: The change of base formula allows us to express log_a(b) in terms of a new base 'c'.
Step 5: The formula states that log_a(b) = log_c(b) / log_c(a). This means you can find log_a(b) by dividing the logarithm of b in base c by the logarithm of a in base c.

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