Rewrite in Terms of Two or More Logarithms Using the Quotient

question 104

Multiple Choice

Rewrite in terms of two or more logarithms using the quotient and product rules for logarithms. Assume all variables
represent positive real numbers.
- $\log 17 \left( \frac { 5 \mathrm {~m} } { \mathrm { y } } \right)$

• A) \(\frac { \log _ { 17 } 5 + \log _ { 17 } \mathrm {~m} } { \log 17 \mathrm { y } }\)
• B) \(\log 175 - \log 17 m - \log 17 \mathrm { y }\)
• C) \(( \log 175 ) ( \log 17 \mathrm {~m} ) - \log 17 \mathrm { y }\)
• D) \(\log 175 + \log 17 m - \log 17 \mathrm { y }\)

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Definitions:

Aromatic Ring

A cyclic molecule with alternating double and single bonds, notable for its stability and presence in many organic compounds.

NMR Spectrum

A representation of the nuclear magnetic resonance, showing the interaction of atomic nuclei with an applied magnetic field, used to determine molecular structure.

Carbons

The elements that serve as the foundational building blocks in all forms of organic life, represented by the symbol C and known for its ability to form a vast number of compounds.

Acceptable Name

A valid chemical name that conforms to the rules set by the International Union of Pure and Applied Chemistry (IUPAC).