The constant term in the expansion of `(3^(x)-2^(x))/(x^(2))` is

Options

A. `log_(e)3`
B. `(log_(e)6)xx{(log_(e))(3/2)}`
C. `1/2(log_(e)6)xx{(log_(e))(3/2)}`
D. none of these

Explanation

To find the constant term in the expansion of \((3^x - 2^x)/x^2\), we can follow these steps:

### Step 1: Expand \(3^x\) and \(2^x\) using their series expansions
The exponential function can be expanded using the Taylor series:
\[ 3^x = e^{x \ln 3} = 1 + \frac{x \ln 3}{1!} + \frac{(x \ln 3)^2}{2!} + \ldots \]
\[
...