Use the Properties of Logarithms to Rewrite the Expression $\log b \sqrt { \frac { 4 x ^ { 8 } } { z ^ { 4 } } }$

question 20

Multiple Choice

Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent positive real numbers.
- $\log b \sqrt { \frac { 4 x ^ { 8 } } { z ^ { 4 } } }$

• A) \(\log _ { b } 2 \cdot 4 \log _ { b } x - 2 \log _ { b } z\)
• B) \(\sqrt { \log _ { \mathrm { b } } 4 } + \sqrt { \log _ { \mathrm { b } } \mathrm { x } ^ { 8 } } - \sqrt { \log _ { \mathrm { b } } \mathrm { z } ^ { 4 } }\)
• C) \(\log _ { b } 2 + 4 \log _ { b } x - 2 \log _ { b } z\)
• D) \(\left( \log _ { b } 2 + + 4 \log _ { b } x \right) \div 2 \log _ { b } z\)

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Operator

A segment of DNA to which a repressor protein binds, regulating the expression of genes by blocking the attachment of RNA polymerase to the promoter region.

RNA Polymerase

An enzyme that synthesizes RNA from a DNA template, essential for the transcription phase of protein synthesis.

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Regulatory mechanisms in gene expression that control the rate and timing of protein synthesis from mRNA.

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Cellular structures where proteins are synthesized, reading mRNA sequences and assembling amino acids into proteins based on genetic instructions.