From the image, we see a graph of the natural logarithmic function $g(x) = \ln(x)$. The point marked on the graph has the coordinates $(X = 2.76, Y = 1.0152307)$. The task is to write the logarithmic equation associated with the displayed point.

The general form of the logarithmic equation is:

$Y = \ln(X)$

Using the point provided $(X = 2.76, Y = 1.0152307)$, we can directly substitute the $X$-value into the equation:

$Y = \ln(2.76)$

We can verify the logarithmic equation by checking if $\ln(2.76)$ equals the given $Y$-value $1.0152307$. Indeed, this is approximately true since:

$\ln(2.76) \approx 1.0152307$

Thus, the logarithmic equation is:

$Y = \ln(2.76)$

Would you like to go over the exponential counterpart of this equation or any other details?

Here are 5 related questions for further exploration:

1. What is the inverse of the logarithmic function $Y = \ln(X)$?
2. How do we rewrite the equation $Y = \ln(X)$ in exponential form?
3. What is the derivative of $g(x) = \ln(x)$?
4. How do the properties of logarithms apply when solving equations like $\ln(a \cdot b)$?
5. What happens to $\ln(x)$ as $x \to 0^+$ or $x \to \infty$?

Tip: The natural logarithm $\ln(x)$ is defined only for positive $x$-values, which is why the graph only appears for $x > 0$.