Can a logarithm have a function as a base? For example is log_(sin(x))(3x) a ridiculous equation? I couldn't find an example on any page about logarithms that used a function on a base, but it seems that for an equation like sin(x)^(12x), the log's base would have to be the sine function. Thank you for the advice!
beninar6u
Answered question
2022-09-08
Can a logarithm have a function as a base? For example is a ridiculous equation? I couldn't find an example on any page about logarithms that used a function on a base, but it seems that for an equation like , the log's base would have to be the sine function. Thank you for the advice!
Answer & Explanation
Jasmin Hoffman
Beginner2022-09-09Added 6 answers
"Can a logarithm have a function as a base ? " Of course not ! But, then again, is not a “function” ! Rather, it is the value of a function — in this case, the sine function — evaluated at point x. These are two different concepts ! Related, to be sure, but different nonetheless. "Is a ridiculous equation ?" Of course not ! In order for an expression to be a “ridiculous equation”, it must be an “equation” first. But I see no equality signs there — do you ? Now that I'm done answering the questions you did ask, allow me to answer the one you never actually asked, but probably meant to all along: Yes, the mathematical expression makes perfect sense, assuming x lies inside positive intervals for which is also positive.