Final answer:
Logarithm of 14 with an undefined base of 1, as in log114, is incorrect, as logarithms with a base of 1 are not valid. If the intended expression is the common logarithm of 14, log(14), it refers to the power 10 must be raised to, which cannot be further simplified without calculation.
Step-by-step explanation:
The student asks to simplify log114 using the power rule of logarithms. The power rule states that logarithm of a number raised to an exponent is the exponent multiplied by the logarithm of the base number, or log(ax) = x · log(a). However, it's important to note that log114 is undefined, as logarithms with a base of 1 are not meaningful because any number to the power of zero equals 1, not the number 14. This may be a typo, and if the student meant log(14), without a specified base, we assume the common logarithm, meaning base 10, and it cannot be simplified further unless we calculate its numerical value.
The common logarithm of a number is the power to which 10 must be raised to equal that number. For numbers less than 1, the common logarithm is negative, as shown in the example log(0.03918) which equals approximately -1.4069. This is because 0.03918 equals 10-1.4069.