Expand the Logarithmic Expression log base p of 78

Problem

(log_p)(78)

Solution

1. Identify the number inside the logarithm, which is 78

2. Find the prime factorization of the number 78 to break it down into smaller factors.

3. Calculate the factors: 78=2×3×13

4. Apply the product rule for logarithms, which states (log_b)(x*y)=(log_b)(x)+(log_b)(y)

5. Expand the expression by writing the logarithm of the product as the sum of the logarithms of its factors.

Final Answer

(log_p)(78)=(log_p)(2)+(log_p)(3)+(log_p)(13)

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