Question

If m> 0 find the value for m such that

\[(424)_{m}= 3\times (123)_{m}\]

Answer 1

Assuming that 3 is in base 10, convert everything else to base 10: (note that m>4)
\[4m^2+2m+4=3(m^2+2m+3)\\
4m^2+2m+4=3m^2+6m+9\\
m^2-4m-5=0\\
(m-5)(m+1)=0\\
m_1=-1; m_2=5 \]
Therefore, m=5.