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 species-area relationship on a logarithmic scale, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Species-Area Relationship**:
The species-area relationship describes how the number of species (species richness, S) increases with the area (A) being considered. The general form of this relationship can be expressed as:
\[ S = C \cdot A^z \]
where:
- \( S \) = species richness
- \( A \) = area
- \( C \) = y-intercept (a constant)
- \( z \) = regression coefficient (indicating the rate of increase of species with area)

2. **Transform to Logarithmic Scale**:
To analyze this relationship on a logarithmic scale, we take the logarithm of both sides of the equation:
\[ \log S = \log (C \cdot A^z) \]

3. **Apply Logarithmic Properties**:
Using the properties of logarithms, we can expand the right side:
\[ \log S = \log C + \log (A^z) \]
Applying the power rule of logarithms, this further simplifies to:
\[ \log S = \log C + z \cdot \log A \]

4. **Final Equation**:
The final equation representing the species-area relationship on a logarithmic scale is:
\[ \log S = \log C + z \cdot \log A \]
This equation indicates that when plotted on a log-log scale, the relationship between log species richness and log area will yield a straight line with slope \( z \) and y-intercept \( \log C \).

5. **Identify the Correct Option**:
Based on the derived equation, the correct representation of the species-area relationship on a logarithmic scale is:
\[ \log S = \log C + z \cdot \log A \]
Therefore, the correct answer is option **b**.