The relation between specises richness and area is described on a logarithmic scale by the equation [where S = species richness, A = area, Z = slope of the line (regression coefficient ), C= Y - intercept]

Options

A. log S = log `C - Z` log A
B. log S = X log A
C. log S = log `C + Z` log A
D. log S = log C

Answer

To solve the question regarding the relationship between species richness (S) and area (A) on a logarithmic scale, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Variables**:
- Identify the variables in the equation:
- S = species richness
- A = area
- Z = slope of the line (regression coefficient)
- C = y-intercept

2. **Starting with the Equation**:
- The relationship is given by the equation:
\[ S = C \cdot A^Z \]

3. **Taking the Logarithm**:
- To express this relationship on a logarithmic scale, we take the logarithm of both sides:
\[ \log S = \log C + Z \log A \]

4. **Rearranging the Equation**:
- This can be rearranged to show the relationship clearly:
\[ \log S = \log C + Z \log A \]
- This indicates that the logarithm of species richness (log S) is a linear function of the logarithm of area (log A).

5. **Interpreting the Graph**:
- The graph of this equation would show species richness (log S) on the y-axis and area (log A) on the x-axis. The slope of the line is Z, and the y-intercept is log C.

6. **Conclusion**:
- The final equation that describes the relationship between species richness and area on a logarithmic scale is:
\[ \log S = \log C + Z \log A \]