How do we calculate log(1024)?

To calculate log(1024), we follow these steps in detail:

Step 1: Understand the base of the logarithm
If no base is specified, the logarithm is assumed to be base 10 (common logarithm). Thus, we are solving for log₁₀(1024).

Step 2: Approximate using a calculator or estimation
Logarithms are generally calculated using a scientific calculator, as base 10 logarithms of arbitrary numbers are not typically integers.

For log₁₀(1024), the exact value can be obtained using a calculator:

log₁₀(1024) ≈ 3.0103

This result means that 10 raised to the power of approximately 3.0103 equals 1024.

Step 3: Verify the calculation (Optional)
To verify, calculate 10³.0103 using a calculator:

10³.0103 ≈ 1024 (approximately correct).

Step 4: Explanation of logarithmic properties
Logarithms help determine how many times the base (10 in this case) must be multiplied by itself to get 1024. Here, it takes a little more than 3 multiplications of 10 (10 × 10 × 10.103 ≈ 1024).

Final Answer:
log₁₀(1024) ≈ 3.0103