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 Alexander von Humboldt's findings on the relationship between species richness and geographical area, we need to identify the correct logarithmic equation that represents this relationship. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Variables
- **S**: Represents the number of species (species richness).
- **A**: Represents the area.
- **C**: A constant that is specific to the habitat.
- **Z**: A constant that represents the slope of the relationship between species richness and area.

### Step 2: Recall the Logarithmic Equation
Alexander von Humboldt's findings can be expressed in a logarithmic form. The general equation that describes the relationship between species richness (S) and area (A) is:
\[ \log S = \log C + z \log A \]
This equation indicates that the logarithm of species richness is a linear function of the logarithm of area.

### Step 3: Rearranging the Equation
The equation can be rearranged to emphasize the relationship:
\[ \log S = \log C + z \log A \]
This shows that as the area (A) increases, the species richness (S) also increases, following a logarithmic relationship.

### Step 4: Identify the Correct Option
From the options provided in the question, we need to find the one that matches the equation:
\[ \log S = \log C + z \log A \]
After reviewing the options, we can determine which one aligns with this equation.

### Conclusion
The correct logarithmic equation for Alexander von Humboldt's findings is:
\[ \log S = \log C + z \log A \]