Alexander von Humboldt gave the relationship between the species richness and its geographical area . Which of the following is the correct logarithmic equation for his findings ?

Options

A. log C = log Z + S log A
B. log C = log C + A log Z
C. log S = log C + Z log A
D. log Z = log C + S log A

Answer

To solve the question regarding the relationship between species richness and geographical area as described by Alexander von Humboldt, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Concept**:
- Alexander von Humboldt proposed a relationship between species richness (the number of different species) and the area of a habitat. This is known as the species-area relationship.

2. **Identifying the Variables**:
- In this relationship, we denote:
- \( S \): Number of species (species richness)
- \( A \): Area
- \( C \): A constant that represents the intercept of the line on the graph
- \( Z \): The slope of the line, which indicates how species richness changes with area.

3. **Formulating the Equation**:
- The relationship can be expressed in a logarithmic form. The general equation for the species-area relationship is:
\[ \log S = \log C + Z \log A \]
- This equation indicates that the logarithm of the number of species is a linear function of the logarithm of the area.

4. **Conclusion**:
- Based on the above understanding, we can conclude that the correct logarithmic equation representing Humboldt's findings is:
\[ \log S = \log C + Z \log A \]

5. **Selecting the Correct Option**:
- If the options provided in the question include this equation, then that option would be the correct answer.