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Can log of the quantity x squared plus y squared be expanded into separate logarithms?
AYes, it becomes 2 log x plus 2 log y
BYes, it becomes log x plus log y
CNo, unless x and y are positive
DNo, sums inside cannot be split
Answer & Solution
Correct answer: D. No, sums inside cannot be split
1. The product, quotient and power rules cover multiplication, division and exponents only.
2. Addition inside the argument matches none of them.
3. So a logarithm of a sum cannot be expanded into separate logarithms.
4. Splitting it into log x plus log y would silently swap the sum for a product.
_Source: OpenStax Precalculus (CC BY 4.0), section 4.5 Logarithmic Properties_