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# $25_r = 23_{10}$ solve for the base r

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Problem Detail:

first of all this is a homework question and I don't want the solution. I just want a reference to how to solve similar questions like this. I believe it's explained my course textbook, "Computer Organization & Architecture: Themes and Variations" but I currently cannot afford the textbook.

Here's the question:

For each of the following numbers, state the base in use; that is, what are the values of r, s, and t?

a. $25_r = 23_{10}$

b. $1001_s = 19684_{10}$

c. $1011_t = 4931_{10}$

I recognize it's similar to solving an equation. I'm guessing I have to find r, s and t and they will be a specific base that matches the base ten number. I tried searching online for similar questions but I'm not sure what to search for so I have no clue where to start for solving these equations.

Any help would be appreciated.

Hint:

Consider $25_{10}$. The number can be written as $5 \cdot 10^0 + 2 \cdot 10^1$.

How can $25_{r}$ be written?