On a logarithmic scale the correct representation of species area relationship is represented by the equation

Options

A. ` Log S = Log C - Z Log A`
B. ` Log S= Log C +Z Log A`
C. `Log A= Log C+ZLog S`
D. `Log S= Log A+Z Log C`

Answer

To solve the question regarding the correct representation of the species-area relationship on a logarithmic scale, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Species-Area Relationship**:
- The species-area relationship describes how the number of species (species richness) increases with the area available. This concept was introduced by Alexander von Humboldt.

2. **Identifying the Basic Equation**:
- The basic equation for the species-area relationship is given as:
\[ S = CA^Z \]
- Here, \( S \) represents species richness, \( A \) is the area, and \( C \) and \( Z \) are constants.

3. **Taking the Logarithm of Both Sides**:
- To represent this relationship on a logarithmic scale, we take the logarithm of both sides of the equation:
\[ \log S = \log (CA^Z) \]

4. **Applying Logarithmic Properties**:
- Using the properties of logarithms, we can expand the right side:
\[ \log S = \log C + \log (A^Z) \]
- Further simplifying gives:
\[ \log S = \log C + Z \log A \]

5. **Final Equation**:
- The final representation of the species-area relationship in logarithmic form is:
\[ \log S = \log C + Z \log A \]
- This equation indicates a linear relationship when plotted on a log-log scale.

6. **Conclusion**:
- The correct representation of the species-area relationship on a logarithmic scale is:
\[ \log S = \log C + Z \log A \]
- This matches option 2 from the question.