To evaluate the expression (48.63 x 8.83)/(18.39 x 3.82) using logarithm tables, we will follow these steps:

• For 48.63:

  • Characteristic: There are 2 digits before the decimal point, so the characteristic is $2-1=1$.
  • Mantissa: Look up 48 under 6, which is 6866. The mean difference for 3 is 3. So, $6866+3 = 6869$.
  • $\log 48.63 = 1.6869$

• For 8.83:

  • Characteristic: There is 1 digit before the decimal point, so the characteristic is $1-1=0$.
  • Mantissa: Look up 88 under 3, which is 9450.
  • $\log 8.83 = 0.9450$

• For 18.39:

  • Characteristic: There are 2 digits before the decimal point, so the characteristic is $2-1=1$.
  • Mantissa: Look up 18 under 3, which is 2625. The mean difference for 9 is 21. So, $2625+21 = 2646$.
  • $\log 18.39 = 1.2646$

• For 3.82:

  • Characteristic: There is 1 digit before the decimal point, so the characteristic is $1-1=0$.
  • Mantissa: Look up 38 under 2, which is 5821.
  • $\log 3.82 = 0.5821$

• Numerator sum: $1.6869 + 0.9450 = 2.6319$
• Denominator sum: $1.2646 + 0.5821 = 1.8467$

• Mantissa: Look for 78 under 5 in the antilog table, which is 6095. The mean difference for 2 is 3. So, $6095+3 = 6098$.
• Characteristic: The characteristic is 0. This means there is $0+1=1$ digit before the decimal point.
• Antilog $0.7852 = 6.098$

Therefore, $X \approx 6.098$.