The given equation is:

$y = 6^{(2x - 3)}$

This is an exponential function where the base is $6$ and the exponent is $2x - 3$.

If you'd like to analyze it further, we can explore the following:

1. Graphing the function: To see how the function behaves for different values of $x$.
2. Solving for $x$: If you want to solve $y = 6^{(2x - 3)}$ for $x$, we can rewrite it in logarithmic form.
3. Finding the derivative: If you are interested in how fast the function changes with respect to $x$, we can compute the derivative.
4. Asymptotic behavior: The function has an asymptote, which we can describe in detail.
5. Transformations: Understanding the effect of shifting and scaling on the graph due to the terms $2x$ and $-3$.

Would you like further details on any of these, or do you have a specific direction you want to explore?

Related Questions:

1. What is the derivative of $y = 6^{(2x - 3)}$?
2. How does the graph of $y = 6^{(2x - 3)}$ look like?
3. How do you solve $6^{(2x - 3)} = k$ for $x$ in terms of $k$?
4. What happens to $y = 6^{(2x - 3)}$ as $x$ approaches infinity or negative infinity?
5. What are the key features (intercepts, asymptotes) of the function $y = 6^{(2x - 3)}$?

Tip:

When solving exponential equations, converting to logarithms is often the most efficient method.