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

beninar6u

Answered question

2022-09-08

Can a logarithm have a function as a base?
For example is log sin ( x ) ( 3 x ) 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 ) 12 x , the log's base would have to be the sine function. Thank you for the advice!

Answer & Explanation

Jasmin Hoffman

Jasmin Hoffman

Beginner2022-09-09Added 6 answers

"Can a logarithm have a function as a base ? "
Of course not ! But, then again, sin ( x ) 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 log sin ( x ) ( 3 x ) 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 log sin x ( 3 x ) = log ( 3 x ) log sin x makes perfect sense, assuming x lies inside positive intervals for which sin x is also positive.

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