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hornejada1c

hornejada1c

Answered question

2022-07-06

log 3 ( 9 )
Can you have a negative base for a logarithm? If the answer is no, why can you not? Isn't the answer to the above just 2?
Similarly, is 3 also a solution to the equation log x ( 9 ) = 2 (I know one solution is obviously 3).

Answer & Explanation

SweallySnicles3

SweallySnicles3

Beginner2022-07-07Added 21 answers

By definition log 3 ( x ) would be the y such that ( 3 ) y = x. The trouble here is that ( 3 ) y is not well-defined unless y is an integer, so you won't be able to solve this for very many different x.
Even if you say that ( 3 ) y is meaningful whenever y is rational with odd denominator, this only gives you countably many different x for which log 3 ( x ) can exist, so it won't behave very much like ordinary logarithms. (The corresponding antilogarithm wouldn't be continuous, for example).
Sonia Ayers

Sonia Ayers

Beginner2022-07-08Added 3 answers

By definition for a > 0 we have
log a ( x ) = log e ( x ) log e ( a )
where
log e ( x ) = 1 x d t t

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