Convert Log10 1000 = 3 to index form.

The general form is $\text{Log}_b x = y \iff b^y = x$.
Here, $b=10$, $x=1000$, and $y=3$.

$$10^3 = 1000$$

Using the general form $\text{Log}_b x = y \iff b^y = x$.
Here, $b=3$, $x=81$, and $y=4$.

$$3^4 = 81$$

Using the general form $\text{Log}_b x = y \iff b^y = x$.
Here, $b=b$, $x=m$, and $y=n$.

$$b^n = m$$

The final answers are:
i. $\boxed{\mathbf{10^3 = 1000}}$
ii. $\boxed{\mathbf{3^4 = 81}}$
iii. $\boxed{\mathbf{b^n = m}}$