Differentiating logarithmsI am trying to prove that f ( x ) = a l o...

skynugurq7

skynugurq7

Answered

2022-07-15

Differentiating logarithms
I am trying to prove that
f ( x ) = a l o g ( x ) => f ( x ) = 1 l n ( a ) x
So I start at
f ( x ) = a l o g ( x )
Then I move to:
f ( x ) = l n ( x ) l n ( a )
And there I get stuck: I want to use the quotient rule, but the entire internet tells me to use the chain rule. And indeed, with the quotient rule I get stuck on an island far away. But still: to me this looks a lot more like:
f ( x ) = g ( x ) h ( x )
Then
f ( x ) = g ( h ( x ) )
So why do I need to use the chain rule from here? How can I use it in this situation?

Answer & Explanation

jugf5

jugf5

Expert

2022-07-16Added 18 answers

No need for the quotient rule: 1 ln ( a ) is a constant.
f ( x ) = ln ( x ) ln ( a ) = 1 ln ( a ) ln ( x ) f ( x ) = 1 ln ( a ) 1 x = 1 ln ( a ) x

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