Start learning →

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_
Practise this question with Quill — NY Regents Algebra II →

Keep practising Properties of Logarithms

Browse all Properties of Logarithms questions for NY Regents Algebra II, or explore more Mathematics topics.

Start a Properties of Logarithms lesson →
Related questions
Fill the three laws of logarithmsExpand log base 3 of (9 times x to the fifth) as far as possible.The logarithm of a product rewrites as which combination of logarithms?