Questions: Evaluate the expression without using a calculator. log 100 log 100 = □ □

To evaluate the expression \(\log 100\) without using a calculator, we need to understand the properties of logarithms, specifically the common logarithm, which is the logarithm with base 10.

The expression \(\log 100\) is asking for the power to which the base 10 must be raised to produce the number 100.

1. Recognize that 100 can be expressed as a power of 10: \[ 100 = 10^2 \]

2. Apply the definition of logarithms: \[ \log_{10} 100 = \log_{10} (10^2) \]

3. Use the logarithmic identity \(\log_b (b^x) = x\): \[ \log_{10} (10^2) = 2 \]

Therefore, the value of \(\log 100\) is 2.

The answer is: \(\log 100 = 2\)