Do the logarithmic rules work when taking logs of functions as opposed to numbers?

Bierlehre59

Bierlehre59

Answered question

2022-08-14

Do the logarithmic rules work when taking logs of functions as opposed to numbers?
i.e. suppose f is a function and n is a real number, is log ( f ( x ) n ) = n · log ( f ( x ) )?

Answer & Explanation

Malierb6

Malierb6

Beginner2022-08-15Added 9 answers

Yes, it will work.
log ( f ( x ) n ) = log ( f ( x ) × f ( x ) . . . × f ( x )
= log ( f ( x ) ) + log ( f ( x ) ) + . . . + log ( f ( x ) )
= n × log ( f ( x ) )
Garrett Sheppard

Garrett Sheppard

Beginner2022-08-16Added 3 answers

Yes, of course.
Because f(x) is still a number for any x.
It even works on expressions: for example log ( ( x 2 + 3 ) 9 ) = 9 log ( x 2 + 3 ) .

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