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Use the rules of logarithms to expand log[ (x+3)⁴ (x-5)⁷ ]someone pls help​

User Kyrubas
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Final answer:

The expression log[(x+3)⁴ (x-5)⁷] is expanded using the logarithm rules for products and exponents to become 4 * log(x+3) + 7 * log(x-5).

Step-by-step explanation:

To expand the expression log[(x+3)⁴ (x-5)⁷] using the rules of logarithms, we can apply two main properties. The first property states that the logarithm of a product of two numbers is the sum of the logarithms of the two numbers. The second relevant property is that the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number.

Using these properties, we can expand the given logarithmic expression as follows:

  • Apply the product rule: log[(x+3)⁴ (x-5)⁷] = log(x+3)⁴ + log(x-5)⁷
  • Apply the exponent rule to both terms: = 4 * log(x+3) + 7 * log(x-5)

This results in the fully expanded form of the original expression, which combines the laws of logarithms concerning products and exponents.

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