Use the Laws of Logarithms to Rewrite the Expression $\ln \frac { e ^ { 3 x } \sqrt { x ^ { 2 } + 1 } } { x ^ { 3 } + y ^ { 3 } }$

question 29

Essay

Use the Laws of Logarithms to rewrite the expression $\ln \frac { e ^ { 3 x } \sqrt { x ^ { 2 } + 1 } } { x ^ { 3 } + y ^ { 3 } }$ in a form with no logarithm of a product, quotient, root, or powers.  

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Definitions:

Photosynthesis

The process by which green plants and some other organisms use sunlight to synthesize nutrients from carbon dioxide and water, releasing oxygen as a byproduct.

Euphotic Zone

The layer of a body of water that is sufficiently lit by sunlight, allowing photosynthesis to occur.

Bathyal Zone

The bathyal zone refers to the oceanic depth range from 200 to 4000 meters below the surface, characterized by limited sunlight and cooler temperatures, inhabiting a unique marine life.

Coastal Zone

The interface between land and water, including the shoreline and adjacent land areas that directly affect or are affected by marine processes.