Assume That X Is a Positive Number $\log _ { b } \frac { x ^ { 2 } + 8 } { x }$

question 143

Multiple Choice

Assume that x is a positive number.Use the properties of logarithms to write the expression
Log_b (x + 8) - log_b x as the logarithm of one quantity.

• A) \(\log _ { b } \frac { x ^ { 2 } + 8 } { x }\)
• B) \(\log _ { b } \frac { x + 8 } { x }\)
• C) \(\log _ { b } \frac { x - 8 } { x }\)
• D) \(\log _ { b } \frac { x ^ { 2 } + 8 } { 8 }\)
• E)log_b (x² - 8x)

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Definitions:

Phosphate Group

A functional group consisting of a phosphorus atom bonded to four oxygen atoms, crucial in the structure of DNA and energy transfer.

Antioxidant Molecules

Compounds that prevent oxidation, a chemical reaction that can produce free radicals and thus damage cells.

Free Radicals

Highly reactive molecules with unpaired electrons that can cause damage to cells and DNA, playing a role in aging and various diseases.

Aerobic Respiration

Oxygen-requiring cellular respiration; breaks down organic molecules (particularly glucose) and produces ATP, carbon dioxide, and water. Includes glycolysis, acetyl–CoA formation, the Krebs cycle, and electron transfer phosphorylation.