If 251m = 100 exttwo, find the value of m.

Here are the solutions to the questions from the image:

1a. If $251_m = 100_{\text{two}}$. Find the value of m

Step 1: Convert both numbers to base 10.
For $251_m$:

$$2 \times m^2 + 5 \times m^1 + 1 \times m^0 = 2m^2 + 5m + 1$$

For $100_{\text{two}}$:

$$1 \times 2^2 + 0 \times 2^1 + 0 \times 2^0 = 4 + 0 + 0 = 4$$

Step