Final answer:
The value of log381 is 4 because 3 raised to the power of 4 equals 81. Logarithms determine the exponent that a base number must be raised to in order to obtain a specific value.
Step-by-step explanation:
The question you've asked is about calculating the value of a logarithm, specifically log381. To find this value, we remember that a logarithm answers the question: 'To what power must the base (in this case, 3) be raised to produce the given number (here, 81)?' Since 34 = 81, the value of log381 is 4.
Moreover, it is important to understand that the common logarithm (log base 10) of a number less than 1 has a negative value. For example, the logarithm of 0.03918 is approximately -1.4069, which can be expressed as 0.03918 = 10-1.4069.