Confusion between exponential functions e.g. $10^x$ and $e^x$

Question

Assume we we have the following exponential function: $10^x$
If we think about it across the x-axis in $0$ the height of the $y$ axis is $1$ and where $x = 1$ it is $10$.
Now if we split the $[0,1]$ to subintervals of $\frac{1}{1000}$ where the function grows we know

1. we need $1000$ such intervals to reach from $0$ to $1$
2. The function grows with the rate of $1 + \frac{2305}{1,000,000}$ since we know that $(1 + \frac{2305}{1,000,000})^{1000} = 1.002305^{1000} \approx 10$. This is based on $\sqrt [1000]{10} = 1.00230523808$

Now if I simplify a bit what is mentioned in $2$ we get $1 + \frac{2305}{1,000,000}\approx 1 + \frac{2000}{1,000,000} = 1 + \frac{1}{500} = 1 + \frac{1}{n}$ so it is a form of $(1 + \frac{1}{n})^n$ which we know that for larger numbers of $n$ this equals $2.71828... = e$

But this is the $10^x$ function and when $n$ reaches $1000$ it should be equal $10$.
So where am I making a mistake here?