The given equation is \(13_m+ 24_m = 41_m\), where m is the base. We can convert these numbers from base m to base 10 to solve for m.

The number \(13_m\) in base 10 is equal to \(1m^1 + 3m^0 = m + 3\).

The number \(24_m\) in base 10 is equal to \(2m^1 + 4m^0 = 2m + 4\).

The number \(41_m\) in base 10 is equal to \(4m^1 + 1m^0 = 4m + 1\).

So, the equation \(13_m+ 24_m = 41_m\) becomes \((m + 3) + (2m + 4) = (4m + 1)\), which simplifies to \(3m + 7 = 4m + 1\).

Solving this equation for m, we get m = 6.