Common Logarithm Mistakes

Mistake One: Distributing the Log

Assuming log(x times y) equals log(x) times log(y). It does not. The correct rule turns a product into a sum, so log base 2 of 32 is 5, not 5 times 5. This is by far the most common error.

Mistake Two: Log of a Negative Number

Trying to find a real log of a negative or zero value. Since no real power of a positive base produces a negative, the log simply does not exist in the reals, and the calculator says so rather than returning a wrong number.

Mistake Three: Using Base 1

Entering a base of 1 and expecting an answer. Every power of 1 is 1, so no exponent can produce any other value, and the logarithm is undefined there.

Mistake Four: Confusing Base and Exponent

Reading log base 2 of 8 as two to the power of 8. The base is the number being raised to a power and the argument is the value you are given. That expression means three.

Mistake Five: Believing the Answer Should Be Whole

Expecting whole numbers always. Log base 10 of 500 is about 2.699, which is perfectly correct. Only exact powers of the base give whole results.

Mistake Six: Trusting Floating Point Exactly

Reading 2.9999999999999996 as meaningfully different from 3. Numbers like 8 and 2 cannot be stored exactly in binary, so dividing their natural logs leaves a tiny remainder. When your inputs are exact, the answer is the whole number.