Find the complete logarithm of the following numbers: 4321 6.00 34.56

To find the complete logarithm of the given numbers, we will calculate $\log_{10}(x)$ for each number, identifying the characteristic and mantissa.

1. For 4321:

   Step 1: Convert to scientific notation. $4321 = 4.321 \times 10^3$

   Step 2: Identify the characteristic and mantissa.

   • Characteristic: $3$
   • Mantissa: $\log_{10}(4.321)$

   Step 3: Calculate the mantissa. Using a calculator: $\log_{10}(4.321) \approx 0.636$

   Step 4: Combine the characteristic and mantissa. $\log_{10}(4321) = 3 + 0.636 = 3.636$

   Final answer: $\boxed{3.636}$

2. For 6.00:

   Step 1: Convert to scientific notation. $6.00 = 6.00 \times 10^0$

   Step 2: Identify the characteristic and mantissa.

   • Characteristic: $0$
   • Mantissa: $\log_{10}(6.00)$

   Step 3: Calculate the mantissa. Using a calculator: $\log_{10}(6.00) \approx 0.778$

   Step 4: Combine the characteristic and mantissa. $\log_{10}(6.00) = 0 + 0.778 = 0.778$

   Final answer: $\boxed{0.778}$

3. For 34.56:

   Step 1: Convert to scientific notation. $34.56 = 3.456 \times 10^1$

   Step 2: Identify the characteristic and mantissa.

   • Characteristic: $1$
   • Mantissa: $\log_{10}(3.456)$

   Step 3: Calculate the mantissa. Using a calculator: $\log_{10}(3.456) \approx 0.539$

   Step 4: Combine the characteristic and mantissa. $\log_{10}(34.56) = 1 + 0.539 = 1.539$

   Final answer: $\boxed{1.539}$