Assume That X, Y, Z and B Are Positive Numbers $\log _ { b } \sqrt [ 4 ] { \frac { x ^ { 5 } y ^ { 2 } } { z ^ { 4 } } }$

question 197

Multiple Choice

Assume that x, y, z and b are positive numbers.Use the properties of logarithms to write the expression $\log _ { b } \sqrt [ 4 ] { \frac { x ^ { 5 } y ^ { 2 } } { z ^ { 4 } } }$ in terms of the logarithms of x, y, and z.

• A) \(\frac { 5 } { 4 } \log _ { b } x + \log _ { b } y - \log _ { b } z\)
• B) \(\frac { 5 } { 4 } \log _ { b } x + \frac { 1 } { 2 } \log _ { b } y - \log _ { b } z\)
• C) \(\log _ { b } x + \frac { 1 } { 2 } \log _ { b } y - \log _ { b } z\)
• D) \(\frac { 5 } { 4 } \log _ { b } ( x + y + z )\)
• E) \(20 \log _ { b } x + 8 \log _ { b } y - 16 \log _ { b } z\)

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Definitions:

Innovation

Innovation involves the introduction of new ideas, goods, services, and processes to the market, playing a crucial role in economic growth and competitiveness.

New Method

An innovative or an improved way of accomplishing tasks or processes, often leading to increased efficiency or effectiveness.

Working Prototype

An initial version of a product that has enough features to allow for the testing and validation of core design concepts.

Invention

This is the creation of a new product, process, or idea that did not exist before.